CBSE Class 10 Mathematics Circles MCQs Set B

Question: In the given figure, ABCD is a cyclic quadrilateral and AB is the diameter. ∠ADC = 140°, then find m ∠BAC

a) 45°
b) 40°
c) 50°
d) none of the options
Answer: c

Question: In the fig, RTP and STQ are common tangents to the two circels with centres A and B. The radii of the two circles are 3 cm and 5 cm respectively. If ST : TQ = 1 : 3 and RT = 4 cm. Find the length of QT and AB.

a) 11 cm, 12 cm
b) 12 cm, 18 cm
c) 18 cm, 12 cm
d) 12 cm, 15 cm
Answer: b

Question: PQ is a chord of a circle .the tangent XR at X on the circle cuts PQ produced at R. If XR = 12 cm , PQ = x cm, QR = (x - 2)cm , find x in cm.
a) 6
b) 7
c) 10
d) 14
Answer: c

Question: In the given figure, AB is the diameter, m ∠BAD = 70° and m ∠DBC = 30°. Find m ∠BDC

a) 25°
b) 30°
c) 40° 
d) 60°
Answer: c

Question: In the given figure, O is the centre of the circle and ∠AOC = 100°. Find the ratio of m ∠ADC : m ∠ABC

a) 5 : 6
b) 1 : 2
c) 5 : 13
d) none of the options
Answer: c

Question: In the given fig. PQ is a tangent to the circle at A, ∠BAQ = 50° and ∠BAC = 35°, then ABC=

a) 50°
b) 35°
c) 85°
d) 95°
Answer: d

Question: DABC and DDBC have a common base and drawn towards one sides. ∠BAC = ∠BDC = 60°. If AC and DB intersect at P, then :

a) AP x PC = BP x PD
b) AP x BP = PC x PD
c) AP x PD = PC x BP
d) none of the options
Answer: a

Question: In the given figure, PAQ is the tangent. BC is the diameter of the circle. m ∠BAQ = 60°, find m ∠ABC

a) 25°
b) 30°
c) 45°
d) 60°
Answer: b

Question: In the given figure, APB is tangent, ∠QPS = 80°, ∠PSQ=65° and ∠SQR = 25°, then

a) ∠SPB = 35°
b) ∠APQ = 65°
c) ∠QSR = 55°
d) all of these
Answer: d

Question: In the given figure the two chords AC and BC are equal. The radius OC intersect AB at M, then AM : BM is :

a) 1 : 1
b) √2 : 3
c) 3 : 2
d) none of the options
Answer: a

Question: If ∠APO = 18°, find ∠AOB.
a) 24°
b) 144°
c) 108°
d) 1 75°
Answer: b

Question: The line AB is 6 m in length and is tangent to the inner one of the two concentric circle at point C. It is known that the radii of the two circles are integers. The radius of the outer circle.

a) 5 m
b) 4 m
c) 6 m
d) 3 m
Answer: a

Question: What is the number of common tangents that can be drawn to two intersecting circles touching at two points?
a) 2
b) 4
c) 3
d) 1
Answer: a 

Question: If the diagonals of a cyclic quadrilateral are equal, then the quadrilateral is
a) rhombus
b) square
c) rectangle
d) none
Answer: c

Question: In the given figure, ∠COB = 40°, AB is the diameter of the circle. Find m ∠CAB:

a) 40°
b) 20°
c) 30°
d) none of the options
Answer: b

Question: In the above question (no. 3) what is the ratio of AM : BM?
a) 5 : 6
b) 3 : 2
c) 1 : 1
d) can't be determined
Answer: c

Question: In the given figure, O is the centre of the circle and, ∠AOB = 100°. Find m ∠BCD :

a) 80°
b) 60°
c) 50°
d) 40°
Answer: c

Question: In the given figure, DABC is an equilateral triangle. Find m ∠BEC:

a) 120°
b) 60°
c) 80°
d) none of the options
Answer: a

Question: PT is a tangent and PAB is a secant of the circle meeting the circle at A and B. If PA = 4 cm and AB = 5 cm. What is the length of PT?
a) 8 cm
b) 6 cm
c) 3 cm
d) 1 cm
Answer: b

Question: In the adjoining figure, O is the centre of circle and diameter AC = 26 cm. If chord AB = 10 cm, then the distance between chord AB and centre O of the circle is :

a) 24 cm
b) 16 cm
c) 12 cm
d) none of the options
Answer: c

Question: Find the distance of a perpendicular from the centre of a circle to the chord if the diameter of the circle is 30 cm and its chord is 24 cm.
a) 6 cm
b) 7 cm
c) 9 cm
d) 10 cm
Answer: c

Question: The quadrilateral formed by angle bisectors of a cyclic quadrilateral is a:
a) rectangle
b) square
c) parallelogram
d) cyclic quadrilateral
Answer: d

Question: In the given figure, O is the centre of the circle. ∠ABO = 60°. Find the value of ∠ACB :

a) 40°
b) 60°
c) 50°
d) 30°
Answer: d

Question: In the adjoining figure, O is the centre of the circle and ∠OBD = 50°. Find the m ∠BAD:
a) 60°
b) 40°
c) 80°
d) 45°
Answer: b

Question: In the given figure OM ^ AB, radius of the circle is 5 cm and length of the chord AB = 8 cm. Find the measure of OM :

a) 3 cm
b) 2.5 cm
c) 2 cm
d) 6 cm
Answer: a

Question: In the given figure, O is the centre of the circle and ∠ACB = 25°. Find ∠AOB :

a) 25°
b) 50°
c) 75°
d) 60°
Answer: b

Question: In the given figure, O is the centre of the circle. Radius of the circle is 17 cm. If OC = 8 cm, then the length of the chord AB is :

a) 35 cm
b) 30 cm
c) 15 cm
d) 18 cm
Answer: b

Question: In the given figure, AB is the diameter of the circle. Find the value of ∠ACD :

a) 30°
b) 60°
c) 45°
d) 25°
Answer: c

Question: In the given figure, ∠BAC and ∠BDC are the angles of same segments. ∠DBC = 30° and ∠BCD = 110°. Find m ∠BAC is :

a) 35°
b) 40°
c) 55°
d) 60°
Answer: b

Question: In the given figure, O is the centre of the circle. ∠AOB = 70°, find m ∠OCD :

a) 70°
b) 55°
c) 65°
d) 110°
Answer: b

Question: O and O' are the centres of two circles which touch each other externally at P. AB is a common tangent. Find ∠APO:
a) 90°
b) 120°
c) 60°
d) data insufficient
Answer: a

Question: In the given figure, chords AB and CD are equal. If ∠OBA = 55° , then m ∠COD is:

a) 65°
b) 55°
c) 70°
d) 50° A
Answer: c

Question: In the given figure, O is the centre of the circle. ∠AOB = 90°. Find m ∠APB :

a) 130°
b) 150°
c) 135°
d) can't be determined
Answer: c

Question: In the given figure, ABC is an isosceles triangle in which AB = AC and m ∠ABC = 50°, m ∠BDC:

a) 80°
b) 60°
c) 65°
d) 100°
Answer: a

Question: In the given figure, AB is the diameter of the circle. ∠ADC = 120°, Find m ∠CAB.

a) 20°
b) 30°
c) 40°
d) Can't be determined.
Answer: b

Question: Find the value of ∠DCE : 

a) 100°
b) 80°
c) 90°
d) 75°
Answer: b

Question: AB and CD are two parallel of a circle such that AB=10 cm and CD = 24 cm. The chords are on opposite sides of the centre and the distance between them is 17 cm. Find the radius of the circle
a) 11 cm
b) 12 cm
c) 13 cm
d) 14 cm
Answer: c

Question: In the given figure, ∠AOC = 120°. Find m ∠CBE, where O is the centre:

a) 60°
b) 100°
c) 120°
d) 150°
Answer: c

Question: In the given figure, there are two circles with the centres O and O' touching each other internally at P. Tangents TQ and TP are drawn to the larger circle and tangents TP and TR are drawn to the smaller circle. Find TQ : TR

a) 8 : 7
b) 7 : 8
c) 5 : 4
d) 1 : 1
Answer: d

Question: In the given figure, AB is diameter of the circle. C and D lie on the semicircle. ∠ABC = 65° and ∠CAD = 45°. Find m ∠DCA. 

a) 45°
b) 25°
c) 20°
d) none of the options
Answer: c

Question: In the given figure, ∠CAB = 40° and ∠AKB = 105°. Find ∠KCD :

a) 65°
b) 35°
c) 40°
d) 72°
Answer: b

Question: In the given figure, ABCD is a cyclic quadrilateral and diagonals bisect each other at P. If ∠DBC = 60° and ∠BAC = 30°, then ∠BCD is :

a) 90°
b) 60°
c) 80°
d) none of the options
Answer: a

Question: ABCD is a cyclic quadrilateral PQ is a tangent at B. If ∠DBQ = 65° , then ∠BCD is : 

a) 35°
b) 85°
c) 115°
d) 90°
Answer: c

Question: In the given figure, O is the centre of the circle. AB is tangent. AB = 12 cm and OB = 13 cm. Find OA:

a) 6.5 cm
b) 6 cm
c) 5 cm
d) none of the options
Answer: c

Question: In a circle of radius 5 cm, AB and AC are the two chords such that AB = AC = 6 cm. Find the length of the chord BC.
a) 4.8 cm
b) 10.8 cm
c) 9.6 cm
d) none of the options
Answer: c