{"id":592314,"date":"2022-04-25T05:22:37","date_gmt":"2022-04-25T05:22:37","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=592314"},"modified":"2022-04-25T10:44:22","modified_gmt":"2022-04-25T10:44:22","slug":"selina-class-10-icse-solutions-mathematics-chapter-17-circles","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/selina-class-10-icse-solutions-mathematics-chapter-17-circles\/","title":{"rendered":"Selina Class 10 ICSE Solutions Mathematics : Chapter 17-\u00a0Circles"},"content":{"rendered":"\n

Class 10: Maths Chapter 17 solutions. Complete Class 10 Maths Chapter 17 Notes.<\/p>\n\n\n\n

Selina Class 10 ICSE Solutions Mathematics : Chapter 17- Circles<\/h2>\n\n\n\n

Selina 10th Maths Chapter 17, Class 10 Maths Chapter 17 solutions<\/p>\n\n\n\n

Exercise 17A<\/h3>\n\n\n\n

Question 1.
In the given figure, O is the centre of the circle. \u2220OAB and \u2220OCB are 30\u00b0 and 40\u00b0 respectively. Find \u2220AOC. Show your steps of working.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 2.
In the given figure, \u2220BAD = 65\u00b0, \u2220ABD = 70\u00b0, \u2220BDC = 45\u00b0<\/strong>
(i) Prove that AC is a diameter of the circle.
(ii) Find \u2220ACB.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 3.
Given O is the centre of the circle and \u2220AOB = 70\u00b0. Calculate the value of:<\/strong>
(i) \u2220 OCA,
(ii) \u2220OAC.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 4.
In each of the following figures, O is the centre of the circle. Find the values of a, b, and c.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 5.
In each of the following figures, O is the centre of the circle. Find the value of a, b, c and d.
\"Selina
Solution:<\/strong>
\"Selina
\"Selina<\/p>\n\n\n\n

Question 6.
In the figure, AB is common chord of the two circles. If AC and AD are diameters; prove that D, B and C are in a straight line. O1<\/sub> and O2<\/sub> are the centres of two circles.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 7.
In the figure given beow, find :<\/strong>
(i) \u2220 BCD,
(ii) \u2220 ADC,
(iii) \u2220 ABC.
\"Selina
Show steps of your workng.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 8.
In the given figure, O is centre of the circle. If \u2220 AOB = 140\u00b0 and \u2220 OAC = 50\u00b0; find :<\/strong>
(i) \u2220 ACB,
(ii) \u2220 OBC,
(iii) \u2220 OAB,
(iv) \u2220CBA
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 9.
Calculate :<\/strong>
(i) \u2220 CDB,
(ii) \u2220 ABC,
(iii) \u2220 ACB.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 10.
In the figure given below, ABCD is a eyclic quadrilateral in which \u2220 BAD = 75\u00b0; \u2220 ABD = 58\u00b0 and \u2220ADC = 77\u00b0. Find:<\/strong>
(i) \u2220 BDC,
(ii) \u2220 BCD,
(iii) \u2220 BCA.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 11.
In the following figure, O is centre of the circle and \u2206 ABC is equilateral. Find :<\/strong>
(i) \u2220 ADB
(ii) \u2220 AEB
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 12.
Given\u2014\u2220 CAB = 75\u00b0 and \u2220 CBA = 50\u00b0. Find the value of \u2220 DAB + \u2220 ABD
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 13.
ABCD is a cyclic quadrilateral in a circle with centre O.
If \u2220 ADC = 130\u00b0; find \u2220 BAC.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 14.
In the figure given below, AOB is a diameter of the circle and \u2220 AOC = 110\u00b0. Find \u2220 BDC.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 15.
In the following figure, O is centre of the circle,
\u2220 AOB = 60\u00b0 and \u2220 BDC = 100\u00b0.
Find \u2220 OBC.<\/strong>
\"Selina<\/p>\n\n\n\n

Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 16.
ABCD is a cyclic quadrilateral in which \u2220 DAC = 27\u00b0; \u2220 DBA = 50\u00b0 and \u2220 ADB = 33\u00b0.
Calculate :<\/strong>
(i) \u2220 DBC,
(ii) \u2220 DCB,
(iii) \u2220 CAB.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 17.
In the figure given alongside, AB and CD are straight lines through the centre O of a circle. If \u2220AOC = 80\u00b0 and \u2220CDE = 40\u00b0. Find the number of degrees in:<\/strong>
(i) \u2220DCE;
(ii) \u2220ABC.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 17 (old).
In the figure given below, AB is diameter of the circle whose centre is O. Given that:
\u2220 ECD = \u2220 EDC = 32\u00b0.
\"Selina
Show that \u2220 COF = \u2220 CEF.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 18.
In the figure given below, AC is a diameter of a circle, whose centre is O. A circle is described on AO as diameter. AE, a chord of the larger circle, intersects the smaller circle at B. Prove that AB = BE.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 19.
In the following figure,<\/strong>
(i) if \u2220BAD = 96\u00b0, find BCD and
(ii) Prove that AD is parallel to FE.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 20.
Prove that:<\/strong>
(i) the parallelogram, inscribed in a circle, is a rectangle.
(ii) the rhombus, inscribed in a circle, is a square.
Solution:
<\/strong>\"Selina
\"Selina<\/p>\n\n\n\n

Question 21.
In the following figure, AB = AC. Prove that DECB is an isosceles trapezium.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 22.
Two circles intersect at P and Q. Through P diameters PA and PB of the two circles are drawn. Show that the points A, Q and B are collinear.
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 23.
The figure given below, shows a circle with centre O. Given: \u2220 AOC = a and \u2220 ABC = b.<\/strong>
(i) Find the relationship between a and b
(ii) Find the measure of angle OAB, if OABC is a parallelogram.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 24.
Two chords AB and CD intersect at P inside the circle. Prove that the sum of the angles subtended by the arcs AC and BD as the centre O is equal to twice the angle APC.
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 24 (old).
ABCD is a quadrilateral inscribed in a circle having \u2220A = 60\u00b0; O is the centre of the circle. Show that: \u2220OBD + \u2220ODB = \u2220CBD + \u2220CDB
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 25.
In the figure given RS is a diameter of the circle. NM is parallel to RS and \u2220MRS = 29\u00b0
Calculate:<\/strong>
(i) \u2220RNM;
(ii) \u2220NRM.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 26.
In the figure given alongside, AB || CD and O is the centre of the circle. If \u2220 ADC = 25\u00b0; find the angle AEB. Give reasons in support of your answer.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 27.
Two circles intersect at P and Q. Through P, a straight line APB is drawn to meet the circles in A and B. Through Q, a straight line is drawn to meet the circles at Cand D. Prove that AC is parallel to BD.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 28.
ABCD is a cyclic quadrilateral in which AB and DC on being produced, meet at P such that PA = PD. Prove that AD is parallel to BC.
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 29.
AB is a diameter of the circle APBR as shown in the figure. APQ and RBQ are straight lines. Find:<\/strong>
(i) \u2220PRB
(ii) \u2220PBR
(iii) \u2220BPR.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 30.
In the given figure, SP is the bisector of angle RPT and PQRS is a cyclic quadrilateral. Prove that: SQ = SR.<\/strong>
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 31.
In the figure, O is the centre of the circle, \u2220AOE = 150\u00b0, DAO = 51\u00b0. Calculate the sizes of the angles CEB and OCE.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 32.
In the figure, P and Q are the centres of two circles intersecting at B and C. ACD is a straight line. Calculate the numerical value of x.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 33.
The figure shows two circles which intersect at A and B. The centre of the smaller circle is O and lies on the circumference of the larger circle. Given that \u2220APB = a\u00b0. Calculate, in terms of a\u00b0, the value of:<\/strong>
(i) obtuse \u2220AOB
(ii) \u2220ACB
(iii) \u2220ADB.
Give reasons for your answers clearly.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 34.
In the given figure, O is the centre of the circle and \u2220 ABC = 55\u00b0. Calculate the values of x and y.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 35.
In the given figure, A is the centre of the circle, ABCD is a parallelogram and CDE is a straight line. Prove that \u2220BCD = 2\u2220ABE
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 36.
ABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given \u2220BED = 65\u00b0; calculate:<\/strong>
(i) \u2220 DAB,
(ii) \u2220BDC.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 37.
\u2220 In the given figure, AB is a diameter of the circle. Chord ED is parallel to AB and \u2220 EAB = 63\u00b0; calculate:<\/strong>
(i) \u2220EBA,
(ii) BCD.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 38.
In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and \u2220DCB = 120\u00b0; calculate:<\/strong>
(i) \u2220 DAB,
(ii) \u2220 DBA,
(iii) \u2220 DBC,
(iv) \u2220 ADC.
Also, show that the \u2206AOD is an equilateral triangle.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 39.
In the given figure, I is the incentre of the \u2206 ABC. Bl when produced meets the circumcirle of \u2206 ABC at D. Given \u2220BAC = 55\u00b0 and \u2220 ACB = 65\u00b0, calculate:<\/strong>
(i) \u2220DCA,
(ii) \u2220 DAC,
(iii) \u2220DCI,
(iv) \u2220AIC.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 40.
A triangle ABC is inscribed in a circle. The bisectors of angles BAC, ABC and ACB meet the circumcircle of the triangle at points P, Q and R respectively. Prove that:<\/strong>
(i) \u2220ABC = 2 \u2220APQ
(ii) \u2220ACB = 2 \u2220APR
(iii) \u2220QPR = 90\u00b0 \u2013 12BAC
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 40 (old).
The sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E; the sides DA and CB are produced to meet at F. If \u2220BEC = 42\u00b0 and \u2220BAD = 98\u00b0; calculate:<\/strong>
(i) \u2220AFB,
(ii) \u2220ADC.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 41.
Calculate the angles x, y and z if: x3=y4=z5
\"Selina<\/strong>
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 42.
In the given figure, AB = AC = CD and \u2220ADC = 38\u00b0. Calculate:<\/strong>
(i) Angle ABC
(ii) Angle BEC.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 43.
In the given figure, AC is the diameter of circle, centre O. Chord BD is perpendicular to AC. Write down the angles p, and r in terms of x.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 44.
In the given figure, AC is the diameter of circle, centre O. CD and BE are parallel. Angle AOB = 80\u00b0 and angle ACE = 10\u00b0. Calculate:<\/strong>
(i) Angle BEC;
(ii) Angle BCD;
(iii) Angle CED.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 45.
In the given figure, AE is the diameter of circle. Write down the numerical value of \u2220ABC + \u2220CDE. Give reasons for your answer.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 46.
In the given figure, AOC is a diameter and AC is parallel to ED. If \u2220CBE = 64\u00b0, calculate \u2220DEC.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 47.
Use the given figure to find<\/strong>
(i) \u2220BAD
(ii) \u2220DQB.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 48.
In the given figure, AOB is a diameter and DC is parallel to AB. If \u2220 CAB = x\u00b0; find (in terms of x) the values of:<\/strong>
(i) \u2220COB
(ii) \u2220DOC
(iii) \u2220DAC
(iv) \u2220ADC.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 49.
In the given figure, AB is the diameter of a circle with centre O. \u2220BCD = 130\u00b0. Find:<\/strong>
(i) \u2220DAB
(ii) \u2220DBA
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 50.
In the given figure, PQ is the diameter of the circle whose centre is O. Given \u2220ROS = 42\u00b0; calculate \u2220RTS.<\/strong>
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 51.
In the given figure, PQ is a diameter. Chord SR is parallel to PQ. Given that \u2220PQR = 58\u00b0; calcula<\/strong>te
(i) \u2220RPQ
(ii) \u2220STP.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 52.
AOD = 60\u00b0; calculate the numerical values of:
AB is the diameter of the circle with centre O. OD is parallel to BC and \u2220AOD = 60\u00b0; calculate the numerical values of:<\/strong>
(i) \u2220ABD,
(ii) \u2220DBC,
(iii) \u2220ADC.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 53.
In the given figure, the centre of the small circle lies on the circumference of the bigger circle. If \u2220APB = 75\u00b0 and \u2220BCD = 40\u2033; find:<\/strong>
(i) \u2220AOB,
(ii) \u2220ACB,
(iii) \u2220ABD,
(iv) \u2220ADB.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 54.
In the given figure, \u2220BAD = 65\u00b0, \u2220ABD = 70\u00b0 and \u2220BDC = 45\u00b0; find:<\/strong>
(i) \u2220BCD,
(ii) \u2220ACB.
Hence, show that AC is a diameter.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 55.
In a cyclic quadrilateral ABCD, \u2220A : \u2220C = 3 : 1 and \u2220B : \u2220D = 1 : 5; find each angle of the quadrilateral.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 56.
The given figure shows a circle with centre O and \u2220ABP = 42\u00b0. Calculate the measure of<\/strong>
(i) \u2220PQB
(ii) \u2220QPB + \u2220PBQ
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 57.
In the given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other. If \u2220 MAD =x and \u2220BAC = y.<\/strong>
(i) express \u2220AMD in terms of x.
(ii) express \u2220ABD in terms of y.
(iii) prove that : x = y
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 61 (old).
In a circle, with centre O, a cyclic quadrilateral ABCD is drawn with AB as a diameter of the circle and CD equal to radius of the circle. If AD and BC produced meet at point P; show that \u2220APB = 60\u00b0.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Exercise 17B<\/h3>\n\n\n\n

Question 1.
In a cyclic-trapezium, the non-parallel sides are equal and the diagonals are also equal.
Prove it.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 2.
In the following figure, AD is the diameter of the circle with centre 0. chords AB, BC and CD are equal. If \u2220DEF = 110\u00b0, calculate:<\/strong>
(i) \u2220 AFE,
(ii) \u2220FAB.
\"Selina<\/p>\n\n\n\n

Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 3.
If two sides of a cycli-quadrilateral are parallel; prove thet:<\/strong>
(i) its other two side are equal.
(ii) its diagonals are equal.
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 4.
The given figure show a circle with centre O. also, PQ = QR = RS and \u2220PTS = 75\u00b0. Calculate:<\/strong>
(i) \u2220POS,
(ii) \u2220 QOR,
(iii) \u2220PQR.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 5.
In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. calculate the sizes of:<\/strong>
(i) \u2220 AOB,
(ii) \u2220 ACB,
(iii) \u2220ABC.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 6.
In a regular pentagon ABCDE, inscribed in a circle; find ratio between angle EDA and angel ADC.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 7.
In the given figure. AB = BC = CD and \u2220ABC = 132\u00b0, calculate:<\/strong>
(i) \u2220AEB,
(ii) \u2220 AED,
(iii) \u2220COD.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 8.
In the figure, O is the centre of the circle and the length of arc AB is twice the length of arc BC. If angle AOB = 108\u00b0, find:<\/strong>
(i) \u2220 CAB,
(ii) \u2220ADB.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 9.
The figure shows a circle with centre O. AB is the side of regular pentagon and AC is the side of regular hexagon. Find the angles of triangle ABC.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 10.
In the given figire, BD is a side of a regularhexagon, DC is a side of a regular pentagon and AD is adiameter. Calculate:<\/strong>
(i) \u2220 ADC
(ii) \u2220BAD,
(iii) \u2220ABC
(iv) \u2220 AEC.
\"Selina
Solution:
<\/strong>\"Selina
\"Selina<\/p>\n\n\n\n

Exercise 17C<\/h3>\n\n\n\n

Question 1.
In the given circle with diametre AB, find the value of x.<\/strong><\/p>\n\n\n\n

\"Selina
Solution:
<\/strong>\"Selina
\u2220ABD = \u2220ACD = 30\u00b0 (Angle in the same segment)
Now in \u2206 ADB,
\u2220BAD + \u2220ADB + \u2220DBA = 180\u00b0 (Angles of a A)
But \u2220ADB = 90\u00b0 (Angle in a semi-circle)
\u2234 x + 90\u00b0 + 30\u00b0 = 180\u00b0 \u21d2 x + 120\u00b0 = 180\u00b0
\u2234 x= 180\u00b0 \u2013 120\u00b0 = 60\u00b0 Ans.<\/p>\n\n\n\n

Question 1.
In the given figure, O is the centre of the circle with radius 5 cm, OP and OQ are perpendiculars to AB and CD respectively. AB = 8cm and CD = 6cm. Determine the length of PQ.
\"Selina
Solution:<\/strong><\/p>\n\n\n\n

\"Selina<\/figure>\n\n\n\n

Question 2.
In the given figure, ABC is a triangle in which \u2220 BAC = 30\u00b0 Show that BC is equal to the radius of the circum-circle of the triangle ABC, whose centre is O.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 3.
Prove that the circle drawn on any one a the equalside of an isoscele triangle as diameter bisects the base.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 3 (old).
The given figure show two circles with centres A and B; and radii 5 cm and 3cm respectively, touching each other internally. If the perpendicular bisector of AB meets the bigger circle in P and Q, find the length of PQ.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 4.
In the given figure, chord ED is parallel to diameter AC of the circle. Given \u2220 CBE = 65\u00b0, calculate \u2220DEC.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 5.
The quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic. Prove it.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 6.
In the figure, \u2220DBC = 58\u00b0. BD is a diameter of the circle. Calculate:<\/strong>
(i) \u2220BDC
(ii) \u2220BEC
(iii) \u2220BAC
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 7.
D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE. Provet that the points B, C, E and D are concyclic.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 7 (old).
Chords AB and CD of a circle intersect each other at point P such that AP = CP.
Show that: AB = CD.<\/strong>
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 8.
In the given rigure, ABCD is a cyclic eqadrilateral. AF is drawn parallel to CB and DA is produced to point E. If \u2220 ADC = 92\u00b0, \u2220 FAE = 20\u00b0; determine \u2220 BCD. Given reason in support of your answer.
\"Selina<\/strong>
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 9.
If I is the incentre of triangle ABC and Al when produced meets the cicrumcircle of triangle ABC in points D. if \u2220 BAC = 66\u00b0 and \u2220 = 80o.calculate:<\/strong>
(i) \u2220 DBC
(ii) \u2220 IBC
(iii) \u2220 BIC.
\"Selina
Solution:
<\/strong>\"Selina
\"Selina<\/p>\n\n\n\n

Question 10.
In the given figure, AB = AD = DC = PB and \u2220 DBC = x\u00b0. Determine, in terms of x:<\/strong>
(i) \u2220 ABD,
(ii) \u2220 APB.
Hence or otherwise, prove thet AP is parallel to DB.
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 11.
In the given figure; ABC, AEQ and CEP are straight lines. Show that \u2220APE and \u2220 CQE are supplementary.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 12.
In the given, AB is the diameter of the circle with centre O.
\"Selina
If \u2220 ADC = 32\u00b0, find angle BOC.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 13.
In a cyclic-quadrilateral PQRS, angle PQR = 135\u00b0. Sides SP and RQ prouduced meet at point A: whereas sides PQ and SR produced meet at point B.
If \u2220A: \u2220B = 2 : 1;find angles A and B.
Solution:<\/strong>
\"Selina
\"Selina<\/p>\n\n\n\n

Question 17 (old).
If the following figure, AB is the diameter of a circle with centre O and CD is the chord with lengh equal radius OA.
If AC produced and BD produed meet at point p; show that \u2220APB = 60\u00b0
\"Selina
Solution:<\/strong>
\"Selina
\"Selina<\/p>\n\n\n\n

Question 14.
In the following figure, ABCD is a cyclic quadrilateral in which AD is parallel to BC.
\"Selina
If the bisector of angle A meet BC at point E and the given circle at point F, prove that:<\/strong>
(i) EF = FC
(ii) BF =DF
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 15.
ABCD is a cyclic quadrilateral. Sides AB and DC produced meet at point e; whereas sides BC and AD produced meet at point F. I f \u2220 DCF : \u2220F : \u2220E = 3 : 5 : 4, find the angles of the cyclic quadrilateral ABCD.
Solution:<\/strong>
\"Selina
\"Selina<\/p>\n\n\n\n

Question 16.
The following figure shows a cicrcle with PR as its diameter. If PQ = 7 cm and QR = 3RS = 6 cm, Find the perimetre of the cyclic quadrilateral PORS.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 17.
In the following figure, AB is the diameter of a circle with centre O. If chord AC = chord AD.prove that:<\/strong>
(i) arc BC = arc DB
(ii) AB is bisector of \u2220 CAD.
Further if the lenghof arc AC is twice the lengthof arc BC find :
(a) \u2220 BAC
(b) \u2220 ABC
\"Selina
Solution:
<\/strong>\"Selina
\"Selina<\/p>\n\n\n\n

Question 18.
In cyclic quadrilateral ABCD; AD = BC, \u2220 = 30\u00b0 and \u2220 = 70\u00b0; find;<\/strong>
(i) \u2220 BCD
(ii) \u2220BCA
(iii) \u2220ABC
(iv) \u2220 ADC
Solution:
<\/strong>\"Selina
\"Selina<\/p>\n\n\n\n

Question 19.
In the given figure, \u2220ACE = 43\u00b0 and \u2220 = 62\u00b0; find the values of a, b and c.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 20.
In the given figure, AB is parallel to DC, \u2220BCE = 80\u00b0 and \u2220 BAC = 25\u00b0
Find<\/strong>
(i) \u2220 CAD
(ii) \u2220 CBD
(iii) \u2220 ADC
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 21.
ABCD is a cyclic quadrilateral of a circle with centre o such that AB is a diameter of this circle and the length of the chord CD is equal to the radius of the circle..if AD and BC produced meet at P, show that APB =60\u00b0
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 22.
In the figure, given alongside, CP bisects angle ACB. Show that DP bisects angle ADB.
\"Selina
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 23.
In the figure, given below, AD = BC, \u2220 BAC = 30\u00b0 and \u2220 = 70\u00b0 find:<\/strong>
(i) \u2220 BCD
(ii) \u2220 BCA
(iii) \u2220 ABC
(iv) \u2220ADC
\"Selina
Solution:
<\/strong>\"Selina<\/p>\n\n\n\n

Question 24.
In the figure given below, AD is a diameter. O is the centre of the circle. AD is parallel to BC and \u2220CBD = 32\u00b0. Find :<\/strong>
(i) \u2220OBD
(ii) \u2220AOB
(iii) \u2220BED (2016)
Solution:
<\/strong>i. AD is parallel to BC, i.e., OD is parallel to BC and BD is transversal.
\"Selina<\/p>\n\n\n\n

\"Selina<\/figure>\n\n\n\n
\"Selina<\/figure>\n\n\n\n

Question 25.
In the figure given, O is the centre of the circle. \u2220DAE = 70\u00b0. Find giving suitable reasons, the measure of<\/strong>
i. \u2220BCD
ii. \u2220BOD
iii. \u2220OBD
\"Selina
Solution:
<\/strong>\u2220DAE and \u2220DAB are linear pair
So,
\u2220DAE + \u2220DAB = 180\u00b0
\u2234\u2220DAB = 110\u00b0<\/p>\n\n\n\n

Also,
\u2220BCD + \u2220DAB = 180\u00b0\u2026\u2026Opp. Angles of cyclic quadrilateral BADC
\u2234\u2220BCD = 70\u00b0
\u2220BCD = 12 \u2220BOD\u2026angles subtended by an arc on the centre and on the circle
\u2234\u2220BOD = 140\u00b0<\/p>\n\n\n\n

In \u0394BOD,
OB = OD\u2026\u2026radii of same circle
So,
\u2220OBD =\u2220ODB\u2026\u2026isosceles triangle theorem
\u2220OBD + \u2220ODB + \u2220BOD = 180\u00b0\u2026\u2026sum of angles of triangle
2\u2220OBD = 40\u00b0
\u2220OBD = 20\u00b0<\/p>\n\n\n\n

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Selina Class 10 ICSE Solutions Mathematics : Chapter 17- Circles<\/p>\n\n\n\n

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