CBSE Class 9 Maths Circles MCQs Set 02

Question: Two circles of radii 10 cm and 8 cm intersect each other and the length of common chord is 12 cm. The distance between their centres is ________.
a) √7 cm
b) 3 √7 cm
c) 4 √7 cm
d) (8 + 2 √7) cm
Answer: d

Question: In the given figure, O is the centre and SAT is a tangent to the circle at A. If ∠BAT = 30°, find ∠AOB and ∠AQB.

a) 60°, 150°
b) 30°, 150°
c) 60°, 60°
d) None of these
Answer: a

Question: In the following figure, PT is of length 8 cm. OP is 10 cm. Then the radius of the circle is ________

a) 2 cm
b) 18 cm
c) (5/4) cm
d) 6 cm
Answer: d

Question: In the given figure, A and B are the centres of two circles that intersect at X and Y. PXQ is a straight line. If reflex angle QBY = 210°, find obtuse angle PAY.

a) 210°
b) 150°
c) 160°
d) 120°
Answer: b

Question: In the given figure, PT touches the circle at R whose centre is O. Diameter SQ when produced meets PT at P. Given ∠SPR = x° and ∠QRP = y°. Then,

a) x° + 2y° = 90°
b) 2x° + y° = 90°
c) x° + y° = 120°
d) 3x° + 2y° = 120°
Answer: a

Question: Two concentric circles of radii a and b, where a > b, are given. The length of a chord of the larger circle which touches the other circle is
a) √a² − b²
b) 2 √a² − b²
c) √a² + b²
d) 2 √a² + b²
Answer: b

Question: If O is the centre of a circle, AOC is its diameter and B is a point on the circle such that ∠ACB = 50°. If AT is the tangent to the circle at the point A, then ∠BAT =

a) 40°
b) 50°
c) 60°
d) 65°
Answer: b

Question: In the given figure, O is the centre of the circle. If PA and PB are tangents, then the value of ∠AQB is

a) 100°
b) 80° 80° Q
c) 60°
d) 50°
Answer: d

Question: In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6 cm, BC = 7 cm, CD = 4 cm, then AD equals ________.

a) 10 cm
b) 13 cm
c) 11 cm
d) 3 cm
Answer: d

Question: The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the the bigger circle. BD is a tangent to the smaller circle touching it at D. Find the length AD.
a) 19 cm
b) 20 cm
c) 16 cm
d) √105 cm
Answer: a

Question: In the given figure, AB and PQ intersect at M. If A and B are centres of circles then ________.

a) PM = MQ
b) PQ ⊥ AB
c) Both PM = MQ and PQ ⊥ AB
d) PQ = AB
Answer: c

Question: In the given figure, a circle touches the side BC of DABC at P and touches AB and AC produced at Q and R r e s p e c t i v e l y. I f AQ = 5 cm, find the perimeter of DABC.

a) 11 cm
b) 10 cm
c) 6 cm
d) 7 cm
Answer: b

Question: In the given figure, O is the centre of a circle; PQL and PRM are the tangents at the points Q and R respectively and S is a point on the circle such that ∠SQL = 50° and ∠SRM = 60°. Then, find ∠QSR and ∠RPQ.

a) 40°, 140° 
b) 50°, 140°
c) 60°, 120°
d) 70°, 40°
Answer: d

Question: How many tangents can a circle have?
a) 1
b) 2
c) 4
d) Infinite
Answer: d

Question: A circle inscribed in DABC having AB = 10 cm, BC = 12 cm, CA = 28 cm touching sides at D, E, F (respectively). Then AD + BE + CF is ________.

a) 25 cm
b) 20 cm
c) 22 cm
d) 18 cm.
Answer: a

Question: In the given figure, O is the centre of the circle, then ∠XOZ is ________.

a) 2 ∠XZY
b) 2 ∠Y
c) 2 ∠Z
d) 2(∠XZY + ∠YXZ)
Answer: d

Question: Let s denote the semiperimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively ,find BD.
a) s – b
b) 2s + h
c) b + s
d) 3b – s
Answer: a

Question: AB is a chord of length 24 cm of a circle of radius 13 cm. The tangents at A and B intersect at a point C. Find the length AC.
a) 31.2 cm
b) 12 cm
c) 28.8 cm
d) 25 cm
Answer: a

Question: In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. If ∠PBT = 30°, then 
 BA : AT is

a) 3 : 1 P
b) 4 : 1
c) 2 : 1
d) 3 : 2
Answer: c

Question: Match the columns.

a) a) → (p), b) → (r), c) → (q)
b) a) → (r), b) → (q), c) → (p)
c) a) → (q), b) → (r), c) → (p)
d) a) → (r), b) → (p), c) → (q)
Answer: b