Class 10 Maths MCQs Chapter 10 Circles
Question 1. The distance between two parallel tangents of acircle of radius 4 cm is
(a) 2 cm
(b) 4 cm
(c) 6 cm
(d) 8 cm
Answer/ Explanation
2. In the given figure, if ZRPS = 25°, the value of ZROS is
(a) 135°
(b) 145°
(c) 165°
(d) 155°
Answer/ Explanation
3. 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
Answer/ Explanation
4. 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
Answer/ Explanation
5. Number of tangents drawn at a point of the , circle is/are
(a) one
(b) two
(c) none
(d) infinite
Answer/ Explanation
6. The tangents drawn at the extremities of the diameter of a circle are
(a) perpendicular
(b) parallel
(c) equal
(d) none of these
Answer/ Explanation
7. Tangents from an external point to a circle are
(a) equal
(b) not equal
(c) parallel
(d) perpendicular
Answer/ Explanation
8. 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
Answer/ Explanation
MCQ Questions on Circles for Class 10 Question 9. In given figure, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 6 cm then the length of BR is
(a) 6 cm
(b) 5 cm
(c) 4 cm
(d) 3 cm
Answer/ Explanation
10. 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 cm²
(b) 65 cm²
(c) 30 cm²
(d) 32.5 cm²
Answer/ Explanation
MCQ Questions for Class 10 Maths Question 11. In the given figure, AB and AC are tangents to the circle with centre O such that ∠BAC = 40°, then ∠BOC is equal to [AI2011]
(a) 40°
(b) 50°
(c) 140°
(d) 150°
Answer/ Explanation
12. In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then the radius of the circle is [Foreign 2011]
(a) 25 cm
(b) 26 cm
(c) 24 cm
(d) 10 cm
Answer/ Explanation
13. A line through point of contact and passing through centre of circle is known as
(a) tangent
(b) chord
(c) normal
(d) segment
Answer/ Explanation
Maths MCQ for Class 10 Cbse With Answers Pdf Question 14. C (O, r1) and C(O, r2) are two concentric circles with r1 > r2 AB is a chord of C(O, r1) touching C(O, r,2) at C then
(a) AB = r1
(b) AB = r2
(c) AC = BC
(d) AB = r1 + r2
Answer/ Explanation
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
Answer/ Explanation
MCQ Questions for Class 10 Maths Circles Question 16. 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 [NCERT Exemplar Problems]
(a) 60 cm²
(b) 65 cm²
(c) 30 cm²
(d) 32.5 cm²
Answer/ Explanation
17. In figure AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to [NCERT Exemplar Problems]
(a) 4 cm
(b) 2 cm
(c) 2√3 cm
(d) 4√3 cm
Answer/ Explanation
18. In figure if O is 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 [NCERT Exemplar Problems]
(a) 100°
(b) 80°
(c) 90°
(d) 75°
Answer/ Explanation
19. Match the column:
| (1) The tangent at any point of a circle is … | (A) known as tangent to the circle |
| (2) The line containing the radius through the point of contact is … | (B) to the radius through the point of |
| (3) The lengths of tangents drawn from an external point to a circle are… | (C) called the ‘normal’ to circle |
| (4) When two end points of the corresponding chord of a secant coincide, it is … | (D) equal |
(a) 1 → A, 2 → B, 3 → C, 4 → D
(b) 1 → B, 2 → A, 3 → D, 4 → C
(c) 1 → D, 2 → A, 3 → C, 4 → B
(d) 1 → B, 2 → C, 3 → D, 4 → A
Answer/ Explanation
Questions on Circles for Class 10 Question 20. In figure, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to [Delhi 2011]
(a) 100°
(b) 40°
(c) 50°
(d) 90°
Answer/ Explanation
21. In the figure PA and PB are tangents to the circle with centre O. If ∠APB = 60°, then ∠OAB is [Delhi 2011]
(a) 30°
(b) 60°
(c) 90°
(d) 15°
Answer/ Explanation
MCQ Questions for Class 10 Maths With Answer: a
Explaination:
(a) Given ∠APB = 60°
∵ ∠APB + ∠PAB + ∠PBA = 180°
⇒ APB + x + x = 180°
[∵ PA = PB ∴ ∠PAB = ∠PBA = x (say)]
⇒ 60° + 2x = 180°
⇒ 2x = 180° – 60°
⇒ 2x = 120°
⇒ x = 120°2 = 60°
Also, ∠OAP = 90°
⇒ ∠OAB + ∠PAB = 90°
⇒ ∠OAB + 60°= 90°
⇒ ∠OAB = 30°
Maths Multiple Choice Questions With Answers for Class 10 Question 22. In the given figure, TP and TQ are two tangents to a circle with centre O, such that ∠POQ = 110°. Then ∠PTQ is equal to [Foreign 2011]
(a) 55°
(b) 70°
(c) 110°
(d) 90°
Answer/ Explanation
23. Infigure,PQandPRaretangentstoacirclewith centreA. If ∠QPA=27°, then ∠QAR equals to [Foreign 2012]
(a) 63°
(b) 153°
(c) 110°
(d) 90°
Answer/ Explanation
Circles MCQ Class 10 Question 24. In figure if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to [NCERT Exemplar Problems]
(a) 20°
(b) 40°
(c) 35°
(d) 45°
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