CBSE Class 10 Mathematics Circles MCQs Set 03

Question: In the given figure, AP = 3 cm, BA = 5 cm and CP = 2 cm. Find CD :

a) 12 cm
b) 10 cm
c) 9 cm
d) 6 cm
Answer: b

Question: In the given figure, PQ is the tangent of the circle. Line segment PR intersects the circle at N and R.
PQ = 15 cm, PR = 25 cm, find PN

a) 15 cm
b) 10 cm
c) 9 cm
d) 6 cm
Answer: c

Question: In the adjoining circle C (O, r) the degree measure of minor arc AB = 130°. Find the degree measure of major arc :

a) 230°
b) 260°
c) 310° 
d) none of the options
Answer: a

Question: In the given figure, two circles with their respective centres intersect each other at A and B and AB intersects OO' at M, then m ∠OMA is :

a) 60°
b) 80°
c) 90°
d) Can't be determined
Answer: c

Question: Through any given set of four points P,Q, R, S it is possible to draw :
a) atmost one circle
b) exactly one circle
c) exactly two circles
d) exactly three circles
Answer: a

Question: In the given figure, tangent PT = 5 cm, PA = 4 cm, find AB : 

a) 7/ 4 cm
b) 11/ 4 cm
c) 9/ 4cm
d) can't be determined
Answer: c

Question: In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is :
a) 23 cm
b) 30 cm
c) 15 cm
d) none of the options
Answer: b

Question: A circle touches a quadrilateral ABCD. Find the true statement:

a) AB + BC = CD + AD
b) AB + CD = BC + AD
c) BD = AC
d) none of the options
Answer: b

Question: The number of common tangents that can be drawn to two given circles is at the most :
a) 1
b) 2
c) 3
d) 4
Answer: b

Question: Two circles of radii 13 cm and 5 cm touch internally each other. Find the distance between their centres
a) 18 cm
b) 12 cm
c) 9 cm
d) 8 cm
Answer: d

Question: The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of bigger circle. BD is a tangent to the smaller circel touching it at D. Find the length of AD.
a) 15 cm
b) 16 cm
c) 18 cm
d) 19 cm
Answer: d 

Question: In the given figure, AP = 2 cm, BP = 6 cm and CP = 3 cm. Find DP :

a) 6 cm
b) 4 cm
c) 2 cm 
d) 3 cm
Answer: b

Question: Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles :
a) 2 cm, 3 cm, 4 cm
b) 3 cm, 4 cm, 1 cm
c) 1 cm, 2.5 cm, 3.5 cm
d) 1 cm, 2 cm, 4 cm
Answer: a

Question: O and O' are the centres of circle of radii 20 cm and 37 cm. AB = 24 cm. What is the distance OO'? 

a) 51 cm
b) 45 cm
c) 35 cm
d) 48 cm
Answer: a

Question: In the given figure, AB and CD are two common tangents to the two touching circles. If CD = 6 cm, then AB is equal to:

a) 9 cm
b) 15 cm
c) 12 cm
d) none of the options
Answer: c

Question: ABC is a right angled triangle AB = 3 cm, BC = 5 cm and AC = 4 cm, then the inradius of the circle is C 5cm 4cm A B 3cm

a) 1 cm
b) 1.25 cm
c) 1.5 cm
d) none of the options
Answer: a

Question: The chord ED is parallel to the diameter AC, as shown in the figure. The ___ magnitude of ∠CED is equal to

a) 30°
b) 40°
c) 50°
d) 60°
Answer: b

Question: In the given figure, CD is a direct common tangent to two circles intersecting each other at A and B, then: ∠CAD + ∠CBD = ?

a) 120°
b) 90°
c) 360°
d) 180°
Answer: d

Question: In a circle of radius 5 cm, AB and AC are two chords such that AB=AC=6 cm. The distance of the chord BC from centre is 

a) 3.6 cm
b) 1.4 cm
c) 1 cm
d) 4 cm
Answer: b

Question: Three equal circles of unit radius touch each other. Then, the area of the circle circumscribing the three circles is :
a) 6π (2 +√3 )²
b) 6/π ( 2+√3)²
c) π/3 (2+√3)²
d) 3π(2+√3)²
Answer: c

Question: 'O' is the centre of the circle, line segment BOD is the angle bisector of ∠AOC, m ∠COD = 50°. Find m ∠ABC:

 a) 25°
b) 50°
c) 100°
d) 120°
Answer: b

Question: In the given figure, O is the centre of circle. ∠AOB = 80° and ∠AOC = 120°. Find m ∠BAC :

a) 120°
b) 80°
c) 100° C
d) none of the options
Answer: b

Question: A circle has two parallel chords of lengths 6 cm and 8 cm. If the chords are 1 cm apart and the centre is on the same side of the chords, then a diameter of the circle is of length:
a) 5 cm
b) 6 cm
c) 8 cm
d) 10 cm
Answer: d

Question: In the adjoining figure, PQRS is a cyclic quadrilateral and the sides PS and QR are produced to meet at B. Then out of the following the true statement is

a) PR= QS
b) PB=QB
c) PR=QB
d) none of the options
Answer: b

Question: An equilateral triangle has side 2 3 cm. The radius of its circumcircle will be
a) 2 cm
b) 3 cm
c) 3 cm
d) 4 cm
Answer: a

Question: In the diagram, PQ and QR are tangents to the circle centre O, at P and R respectively. Find the value of

a) 25
b) 35
c) 45
d) 55
Answer: c

Question: If AB is a chord of a circle, P and Q are two points on the circle different from A and B, then:
a) the angle subtended by AB at P and Q are either equal or supplementary.
b) the sum of the angles subtended by AB at P and Q is always equal two right angles.
c) the angles subtended at P and Q by AB are always equal.
d) the sum of the angles subtended at P and Q is equal to four right angles.
Answer: a 

Question: In the fig., PQ is a tangent to the circle at P. QRS is a straight line. Find the value of x.

a) 25°
b) 30°
c) 35°
d) 40°
Answer: d

Question: AB is the chord of a circle with centre O. AB is produced to C, such that BC = OB. CO is joined and produced to meet the circle in D. If ∠ACD=y° and ∠AOD = x°, then

a) 3x°=y°
b) x°=3y°
c) x°=y°
d) x°=4y°
Answer: b

One Word Question :

Question: Count the number of tangents in the given figure.

Answer: 3

Question: In figure, if PC=CR, then which two sides of a triangle are equal.

Answer: PQ = QR

Question: In figure AP = 4cm, OA = 3cm, OB = 2cm. Find BP.

Answer: √21cm

Question: How many lines in this figure are not cutting the circle at all?

Answer: 5

Question: If PR=7.5cm, find PS.

Answer: 15cm

Question: In the given figure if AB = 11.5cm and DC = 10.5cm find AD+BC.

Answer: 22cm.

Question: Find OP.

Answer: 7cm

Question: Find x and y.

Answer: x = 40⁰ , y = 50⁰

Question: In figure, ΔABC touches a circle at a point P. If we extend the sides AB and AC, they touch the circle at Q and R respectively. If the perimeter of a triangle is 12cm, find AQ.

Answer: 6cm

Question: In the figure, the sides of a quad. ABCD touch a circle at P, Q, R and S. Then what is (AB+CD) equal to?

Answer: AD+BC

Question: Find BC in the given figure.

Answer: 15cm.

Question: Find perimeter of ΔPQR

Answer: 28cm

Question: In figure, PA and PB are two tangents drawn from a point P to a circle with centre O touching it at A and B. Then complete the statement : OP is the _________ of AB.

Answer: Perpendicular bisector

Question: Find ∠BTQ

Answer: 75°

Question: How many tangents are there in all in this figure?

Answer: 1

Question: Count number of secants in this figure.

Answer: 5

Question: Find perimeter of triangle ABC.

Answer: 56cm

Question: Find BP.

Answer: 4 √10cm

Question: Find ∠ACB

Answer: 550

Question: In figure, A point P is 29cm away from the centre of a circle. Find the length of tangent drawn from P to the circle whose radius is 20cm.

Answer: 21cm