## MCQ Questions for Class 10 Maths: Ch 10 Circles

1. A tangent is drawn from a point at a distance of 17 cm of circle C(0, r) of radius 8 cm. The length of its tangent is

(a) 5 cm

(b) 9 cm

(c) 15 cm

(d) 23 cm

► (c) 15 cm

2. A circle is inscribed in a Î”ABC having AB = 10cm, BC = 12cm and CA = 8cm and touching these sides at D, E, F respectively. The lengths of AD, BE and CF will be

(a) AD = 4cm, BE = 6cm, CF = 8cm

(b) AD = 5cm, BE = 9cm, CF = 4cm

(c) AD = 3cm, BE = 7cm, CF = 5cm

(d) AD = 2cm, BE = 6cm, CF = 7cm

► (c) AD = 3cm, BE = 7cm, CF = 5cm

3. The length of tangents drawn from an external point to the circle

(a) are equal

(b) are not equal

(c) sometimes are equal

(d) are not defined

► (a) are equal

4. The tangents drawn at the extremities of the diameter of a circle are

(a) perpendicular

(b) parallel

(c) equal

(d) none of these

► (b) parallel

5. The length of a tangent drawn from a point at a distance of 10 cm of circle is 8 cm. The radius of the circle is

(a) 4 cm

(b) 5 cm

(c) 6 cm

(d) 7 cm

► (c) 6 cm

6. At point A on a diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY at a distance 16 cm from A is

(a) 8 cm

(b) 10 cm

(c) 16 cm

(d) 18 cm

► (c) 16 cm

7. Segment joining the points of contact of two parallel tangents

(a) may or may not pass through the centre.

(b) will pass through the centre.

(c) will not pass through the centre.

(d) none of these

► (b) will pass through the centre.

8. From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is

(a) 60 cm

^{2}
(b) 65 cm

^{2}
(c) 30 cm

^{2}
(d) 32.5 cm

► (a) 60 cm^{2}^{2}

9. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80° then ∠POA is equal to

(a) 50°

(b) 60°

(c) 70°

(d) 80°

► (a) 50°

10. 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

(a) √119 cm

(b) 13 cm

(c) 12 cm

(d) 8.5 cm

► (a) √119 cm

12. From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is

(a) 60 cm

^{2}
(b) 65 cm

^{2}
(c) 30 cm

^{2}
(d) 32.5 cm

^{2}
► (a) 60 cm

13. A line through point of contact and passing through centre of circle is known as

(a) tangent

(b) chord

(c) normal

(d) segment

► (c) normal

^{2}13. A line through point of contact and passing through centre of circle is known as

(a) tangent

(b) chord

(c) normal

(d) segment

► (c) normal

14. In a circle of radius 7cm, tangent PT is drawn from point P such that PT = 24cm. If O is the centre of the circle, then the length of OP is:

(a) 30cm

(b) 31cm

(c) 28cm

(d) 25cm

► (d) 25cm

15. Two parallel lines touch the circle at points A and B respectively. If area of the circle is 25 n cm2, then AB is equal to

(a) 5 cm

(b) 8 cm

(c) 10 cm

(d) 25 cm

► (c) 10 cm

16. The maximum number of common tangents that can be drawn to two circles intersecting at two distinct point is

(a) 2

(b) 4

(c) 1

(d) 3

► (a) 2

17. Tangents from an external point to a circle are

(a) equal

(b) not equal

(c) parallel

(d) perpendicular

► (a) equal

18. Number of tangents drawn at a point of the , circle is/are

(a) one

(b) two

(c) none

(d) infinite

► (a) one

19. If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal to

(a) 60°

(b) 70°

(c) 80°

(d) 90°

► (b) 70°

20. PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR = 120°, then ∠OPQ is

(a) 60°

(b) 45°

(c) 30°

(d) 90°

► (c) 30°

21. Two circle touch each other externally at C and AB is a common tangent to the circles. Then, ∠ACB =

(a) 60°

(b) 45°

(c) 30°

(d) 90°

► (d) 90°

22. If four sides of a quadrilateral ABCD are tangential to a circle, then

(a) AC + AD = BD + CD

(b) AB + CD = BC + AD

(c) AB + CD = AC + BC

(d) AC + AD = BC + DB

► (b) AB + CD = BC + AD