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