CBSE Class 10 Mathematics Circles MCQs

Question : The common point of a tangent to a circle with the circle is called

(a) Centre
(b) point of contact
(c) end point
(d) none of these.
Answer : B

Question : A tangent PQ at a point P of a circle of radius 5 cm meets a line through the Centre O at a point Q so that OQ = 12 cm. Length PQ is -----
(a) 12 cm
(b) 13 cm
(c) 8.5 cm
(d) √119 cm.
Answer : D

Question : If angle between two radii of a circle is 130º, the angle between the tangents at the ends of the radii is :
(a) 90º
(b) 50º
(c) 70º
(d) 40º
Answer : B

Question : In Fig., if O is the centre of a circle PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is equal to ------

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

Question : If two tangents inclined at an angle of 60ᵒ are drawn to a circle of radius 3cm, then the length of each tangent is equal to
(a) 3√3/ 2 cm
(b) 3cm
(c) 6cm
(d) 3√3cm
Answer : D

Question : A line intersecting a circle in two points is called a _______.
(a) Secant
(b) Chord
(c) Diameter
(d) Tangent
Answer : A

Question : In Fig., AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to

(a) 4 cm
(b) 2 cm
(c) 2√3 cm
(d) 4√3 cm
Answer : C

Question : The number of tangents drawn from a point lies inside the circle is --------
(a) Two tangents
(b) only one tangent
(c) No tangents
(d) Infinite tangents
Answer : C

Question : In the given Fig., AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent to the circle at the point A, the ∠BAT is equal to

(a) 65°
(b) 60°
(c) 40°
(d) 50°
Answer : D

Question : The number of tangents drawn from a point lies on the circle is --------
(a) Two tangents
(b) only one tangent
(c) No tangents
(d) Infinite tangents
Answer : B

Question : A circle can have _____parallel tangents at a single time.
(a) One
(b) Two
(c) Three
(d) Four
Answer : B

Question : In Fig., if ∠AOB = 125°, then ∠COD is equal to
(a) 62.5°
(c) 35°
(b) 45°
(d) 55°
Answer : D

Question : The area of the circle that can be inscribed in a square of each 6cm is
(a) 36π sq.cm
(b) 18π sq.cm
(c) 12 π sq.cm
(d) 9π sq.cm
Answer : D

Question : If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is -----
(a) 3cm
(b) 1cm
(c) 6cm
(d) 9cm
Answer : D

Question : The number of tangents drawn from a point lies outside the circle is --------
(a) Two tangents
(b) only one tangent
(c) No tangents
(d) Infinite tangents 
Answer : A

Question : In the given Fig. if PR = 24 cm and OP = 25 cm, then the radius of circle is :

(a) 7 cm 
(b) 12 cm 
(c) 15 cm
(d) 49 cm 
Answer : A

Question : If the chord of the larger circle of radius b units touches the smaller concentric circle of radius a units, then its length is :
(a) √(a² -b²)
(b) √(b²-a²)
(c) 2√(a²-b²)
(d) 2√(b²-a²) 
Answer : D

Question : Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of a larger circle which touches the smaller circle as given in the fig.

(a) 6 cm
(b) 9 cm 
(c) 8 cm 
(d) 2 cm
Answer : B

Question : To draw a pair of tangents to a circle which are inclined to each other at an angle of 100°, it is required to draw tangents at end points of those two radii of the circle, the angle between which should be
(a) 100°
(b) 50°
(c) 80° 
(d) 260°
Answer : C

Question : The number of tangents that can be drawn to a circle from a point inside the circle is /are :
(a) 1
(b) infinite 
(c) 0 
(d) 2
Answer : C

Question : Distance between two parallel lines is 14 cm, the radius of circle which will touch both lines is
(a) 6 cm 
(b) 7 cm 
(c) 12 cm
(d) 14 cm
Answer : B

Question : The length of the tangent from a point A out side the circle, of radius 3 cm is 4 cm then distance of A from the centre of the circle is
(a) 7 cm
(b) 7 cm 
(c) 5 cm 
(d) 25 cm
Answer : C

Question : The distance between two parallel tangents in a circle of radius 3.5 cm is :
(a) √7 cm 
(b) 14 cm
(c) 3.5 cm
(d) 1.75 cm
Answer : A

Question : AT is a tangent to a circle at A with centre O from an external point T such that OT = 8 cm and ∠OTA = 30°. The length of AT (in cm) is :
(a) √2
(b) 3√2 
(c) 4√3 
(d) 4
Answer : C

Question : In given Fig. O is the centre of a circle of radius 6 cm. At a distance of 10 cm from O, a point P is taken. Two tangents PQ and PR are drawn to the circle from this point. Then area of quadrilateral PQOR is :

(a) 60 cm² 
(b) 28 cm² 
(c) 48 cm² 
(d) 30 cm²
Answer : C

Question : In below Fig, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If Ð DBC =55° and ÐBAC = 45°, find ÐBCD.

(a) 80º (b) 60º (c) 90º (d) none of these

Question : In above sided Fig, A,B and C are three points on a circle with centre O such that ÐBOC = 30° and ÐAOB = 60°. If D is a point on the circle other than the arc ABC, find ÐADC.
(a) 45º
(b) 60º
(c) 90º
(d) none of these

Question : Find the length of tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre.
(a) 24 cm
(b) 27 cm
(c) 26 cm
(d) 25 cm

Question : A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc
(a) 1500
(b) 30º
(c) 60º
(d) none of these

Question : A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.
(a) 1500
(b) 30º
(c) 60º
(d) none of these

Question : In the below Fig., ÐABC = 69°, ÐACB = 31°, find ÐBDC.
(a) 80º
(b) 60º
(c) 90º
(d) 1000

Question : In the above sided Fig., A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ÐBEC = 130° and ÐECD = 20°. Find ÐBAC.
(a) 110º
(b) 150º
(c) 90º
(d) 1000

Question : ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ÐDBC = 70°, ÐBAC is 30°, find ÐBCD.
(a) 80º
(b) 60º
(c) 90º
(d) 1000

Question : ABCD is a cyclic quadrilateral. If ÐBCD = 100°, ÐABD is 30°, find ÐABD.
(a) 80º
(b) 60º
(c) 90º
(d) 700

Question : ABCD is a cyclic quadrilateral. If ÐDBC= 80°, ÐBAC is 40°, find ÐBCD.
(a) 80º
(b) 60º
(c) 90º
(d) 700

Question : A point P is 26 cm away from the centre of a circle and the length of the tangent drawn from P to the circle is 24 cm. Find the radius of the circle.
(a) 11 cm
(b) 10 cm
(c) 16 cm
(d) 15 cm

Question : From an external point P, tangents PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA = 14 cm, find the perimeter of the DPCD.
(a) 28 cm
(b) 27 cm
(c) 26 cm
(d) 25 cm

Question : In the above sided figure, PA and PB are tangents such that PA = 9cm and ÐAPB = 60⁰. Find the length of the chord AB.
(a) 4 cm
(b) 7 cm
(c) 6 cm
(d) 9 cm

Question : In the below figure the circle touches all the sides of a quadrilateral ABCD whose three sides are AB = 6 cm, BC = 7 cm, CD = 4 cm. Find AD.
(a) 4 cm
(b) 3 cm
(c) 6 cm
(d) 9 cm

Question : In the above sided Fig., if TP and TQ are the two tangents to a circle with centre O so that ÐPOQ = 110°, then ÐPTQ is equal to
(a) 60⁰ 
(b) 70⁰ 
(c) 80⁰ 
(d) 90⁰

Question : If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ÐPOA is equal to
(a) 60⁰ 
(b) 70⁰ 
(c) 80⁰ 
(d) 50⁰

Question : The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
(a) 4 cm
(b) 3 cm
(c) 6 cm
(d) 5 cm

Question : From a point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn. Find the radius of the circle.
(a) 4 cm
(b) 7 cm
(c) 6 cm
(d) 5 cm

Question : PT is tangent to a circle with centre O, OT = 56 cm, TP = 90 cm, find OP
(a) 104 cm
(b) 107 cm
(c) 106 cm
(d) 105 cm

Question : TP and TQ are the two tangents to a circle with center O so that angle ÐPOQ = 130°. Find ÐPTQuestion :
(a) 50⁰ 
(b) 70⁰ 
(c) 80⁰ 
(d) none of these

Question : From a point Q, the length of the tangent to a circle is 40 cm and the distance of Q from the centre is 41 cm. Find the radius of the circle.
(a) 4 cm
(b) 3 cm
(c) 6 cm
(d) 9 cm

Question : The common point of a tangent to a circle with the circle is called _________
(a) centre
(b) point of contact
(c) end point
(d) none of these.

Question : PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see below figure). Find the length TP.
(a) 203cm
(b) 10 3cm
(c) 403cm
(d) none of these

Question : The lengths of tangents drawn from an external point to a circle are equal.
(a) half
(b) one third
(c) one fourth
(d) equal

Question : ABCD is a cyclic quadrilateral in which BC is parallel to AD, ÐADC = 1100 and ÐBAC = 500. Find ÐDAC
(a) 80º
(b) 60º
(c) 90º
(d) 1700

Question : In the below figure, ÐPOQ= 800, find ÐPAQ
(a) 80º
(b) 40º
(c) 100º
(d) none of these

Question : In the above figure, ÐPQR = 100°, where P, Q and R are points on a circle with centre O. Find ÐOPR.
(a) 80º
(b) 40º
(c) 10º
(d) none of these