## Class 10 Maths Chapter 10 Circles MCQs

Q1. **A circle has a number of tangents equal to**

(a) 0

(b) 1

(c) 2

(d) Infinite

Answer: **(d) Infinite**

Q2. **A tangent intersects the circle at:**

(a) One point

(b) Two distinct point

(c) At the circle

(d) None of the above

Answer: **(a) One point**

Q3. **If the angle between two radii of a circle is 110º, then the angle between the tangents at the ends of the radii is:**

(a) 90º

(b) 50º

(c) 70º

(c) 40º

Answer: **(c) 70º**

Q4. **The length of the tangent from an external point A on a circle with centre O is**

(a) always greater than OA

(b) equal to OA

(c) always less than OA

(d) cannot be estimated

Answer: **(c) always less than OA**

Q5. **AB is a chord of the circle and AOC is its diameter such that angle ACB = 50°. If AT is the tangent to the circle at the point A, then BAT is equal to**

(a) 65°

(b) 60°

(c) 50°

(d) 40°

Answer: **(c) 50°**

Q6. **If TP and TQ are the 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°

Answer: **(b) 70°**

Q7. **The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is:**

(a) 3 cm

(b) 5 cm

(c) 7 cm

(d) 10 cm

Answer: **(a) 3 cm**

Q8. **If a parallelogram circumscribes a circle, then it is a:**

(a) Square

(b) Rectangle

(c) Rhombus

(d) None of the above

Answer: **(c) Rhombus**

Q9. **Two concentric circles are of radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle is:**

(a) 8 cm

(b) 10 cm

(c) 12 cm

(d) 18 cm

Answer: **(a) 8 cm**

Q10. **If angle between two radii of a circle is 130°, the angle between the tangents at the ends of the radii is**

(a) 90°

(b) 50°

(c) 70°

(d) 40°

Answer: **(b) 50°**

Q11. ** If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to**

(a) (3/2)√3 cm

(b) 6 cm

(c) 3 cm

(d) 3√3 cm

Answer: **(d) 3√3 cm**

Q12. **The tangent to a circle is ___________ to the radius through the point of contact.**

(a) parallel

(b) perpendicular

(c) perpendicular bisector

(d) bisector

Answer: **(b) perpendicular**

Q13. **Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. The radius of the inner circle will be**

(a) 3 cm

(b) 4 cm

(c) 2.5 cm

(d) 2 cm

Answer: **(a) 3 cm**

Q14. **The distance between two parallel tangents of a circle is 18 cm, then the radius of the circle is**

(a) 8 cm

(b) 10 cm

(c) 9 cm

(d) 7.5 cm

Answer: (c) 9 cm

Q15. The tangent is the special case of the secant when the two end points of its corresponding

a) Chord coincide

b) Chord not coincide

c) Both a and b

d) None

Ans: a) chord coincide

Q16. There is no tangent to a circle passing through a point

a) Lying on the circle

b) Lying inside the circle

c) Lying outside the circle

d) None

Ans: b) lying inside the circle

Q17. **There are exactly two tangents to a circle through a point**

a) Lying inside the circle

b) Lying outside the circle

c) Lying on the circle

d) None

Ans: b) lying outside the circle

Q18. **How many tangents are possible to draw through a point which is lying inside the circle**

a) One and only one

b) Exactly two

c) No tangent

d) None

Ans: c) no tangent

Q19. **How many tangents are possible to draw to the circle through a point which is lying outside the circle**

a) One and only one

b) No tangent

c) Exactly two tangents

d) Infinite

Ans: c) exactly two tangents