# MCQ Questions for Class 10 Maths Circles with Answers

## MCQ Questions for Class 10 Maths Circles with Answers

Free PDF Download of CBSE Class 10 Maths Chapter 10 Circles Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Circles MCQs with Answers to know their preparation level.

### Class 10 Maths MCQs Chapter 10 Circles

Circle Multiple Choice 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

Explaination:

Reason: Here radius, r = 4 cm
Required distance,
AB = OA + OB
= r + r = 2r = 2Ã—4 = 8 cm

2. In the given figure, if ZRPS = 25Â°, the value of ZROS is

(a) 135Â°
(b) 145Â°
(c) 165Â°
(d) 155Â°

Circles Class 10 MCQ With Answer: dExplaination: Reason: Since OR âŠ¥ PR and OS âŠ¥ PS
âˆ´ âˆ ORP = âˆ OSP = 90Â°
In â–¡ ORPS, âˆ ROS + âˆ ORP + âˆ RPS + âˆ OSP = 360Â°
âˆ ROS + 90Â° + 25Â° + 90Â° = 360Â°
âˆ ROS = 360Â° â€“ 205Â° = 155Â°

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

Explaination:

Reason: In rt âˆ†OAP, APÂ² + OAÂ² = OPÂ²
â‡’ APÂ² + (8)Â² = (17)Â² => APÂ² + 64 = 289
â‡’ APÂ² = 289 â€“ 64 = 225
âˆ´ AP = âˆš225 = 15 cm

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

Explaination: Reason: Since the length of tangents drawn from an external point to a circle are equal.

5. Number of tangents drawn at a point of the , circle is/are
(a) one
(b) two
(c) none
(d) infinite

Explaination: Reason: There is only one tangent at a point of the circle.

6. The tangents drawn at the extremities of the diameter of a circle are
(a) perpendicular
(b) parallel
(c) equal
(d) none of these

Explaination:

Reason: Since OP âŠ¥ AB and OQ âŠ¥ CD
âˆ´ Z1 = 90Â° and Z2 = 90Â°
â‡’ âˆ 1 = Z2, which are alternate angles.
âˆ´ AB || CD

7. Tangents from an external point to a circle are
(a) equal
(b) not equal
(c) parallel
(d) perpendicular

MCQs of Maths for Class 10 With Answer: aExplaination: Reason: Tangents from external points to a circle are equal.

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

Explaination:

Reason: In rt. AOAP, we have
OAÂ² + APÂ² = OPÂ²
â‡’ OAÂ² + (8)Â² = (10)2
â‡’ OAÂ² + 64 = 100
â‡’ OAÂ² = 100 â€“ 64 = 36
âˆ´ OA = âˆš36 = 6 cm

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

Explaination: Reason: Since
BQ = BR ...(i) [âˆµ Tangents drawn from external points are equal]
CQ = CP ...[Using (i)]
BC + BQ = 11
â‡’ 6 + BR = 11
â‡’ BR = 11 â€“ 6 = 5 cm

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 cmÂ²
(b) 65 cmÂ²
(c) 30 cmÂ²
(d) 32.5 cmÂ²

Explaination:

Reason: OPÂ² = OQÂ² + PQÂ²
169 = 25 + PQÂ²
PQÂ² = 144
PQ = 12
Area PQOR = ar (AOPQ) + ar (AOPR)
= 12 $\frac{1}{2}$ Ã— 12 Ã— 5 + 12 $\frac{1}{2}$ Ã— 12 Ã— 5 = 60 cmÂ²

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 âˆ BAC = 40Â°, then âˆ BOC is equal to [AI2011]

(a) 40Â°
(b) 50Â°
(c) 140Â°
(d) 150Â°

Explaination:
âˆ ABO + âˆ BOC + âˆ OCA + âˆ BAC = 360Â°
â‡’ 90Â° + âˆ BOC + 90Â° + 40Â° = 360Â°
â‡’ âˆ BOC = 360Â° â€“ 220Â° = 140Â°

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

Explaination: (d) v OT is radius and PT is tangent

âˆ´ OT âŠ¥ PT
Now, in AOTP,
â‡’ OPÂ² = PTÂ² + OTÂ²
â‡’ 26Â² = 24Â² + OTÂ²
â‡’ 676 â€“ 576 = OTÂ²
â‡’ 100 = OTÂ²
â‡’ 10 cm = OT

13. A line through point of contact and passing through centre of circle is known as
(a) tangent
(b) chord
(c) normal
(d) segment

Explaination: (c) normal

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

Explaination:
(c) âˆµ AB touches
C(0, r<sub>2</sub>)
âˆ´ OC âŠ¥ AB

Also, perpendicular from the centre to a chord bisects the chord.
âˆ´ AC = BC

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

Explaination:
(c) Let radius of circle = R
âˆ´ Ï€RÂ² = 25Ï€
â‡’ R = 5 cm
âˆ´ Distance between two parallel tangents = diameter = 2 Ã— 5 = 10 cm.

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 cmÂ²
(b) 65 cmÂ²
(c) 30 cmÂ²
(d) 32.5 cmÂ²

Explaination:

17. In figure AT is a tangent to the circle with centre O such that OT = 4 cm and âˆ OTA = 30Â°. Then AT is equal to [NCERT Exemplar Problems]
(a) 4 cm
(b) 2 cm
(c) 2âˆš3 cm
(d) 4âˆš3 cm

Explaination:

18. In figure if O is centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50Â° with PQ, then âˆ POQ is equal to [NCERT Exemplar Problems]

(a) 100Â°
(b) 80Â°
(c) 90Â°
(d) 75Â°

Explaination:
(a) OP âŠ¥ PR [Y Tangent and radius are âŠ¥ to each other at the point of contact]
âˆ OPQ = 90Â° â€“ 50Â° = 40Â°
âˆ´ âˆ OPQ = âˆ OQP = 40Â°
In âˆ†OPQ,
â‡’ âˆ POQ + âˆ OPQ + âˆ OQP = 180Â°
â‡’ âˆ POQ + 40Â° + 40Â° = 180Â°
âˆ POQ = 180Â° â€“ 80Â° = 100Â°.

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 â€˜normalâ€™ to circle (4) When two end points of the corresponding chord of a  secant coincide, it is ... (D) equal

(a) 1 â†’ A, 2 â†’ B, 3 â†’ C, 4 â†’ D
(b) 1 â†’ B, 2 â†’ A, 3 â†’ D, 4 â†’ C
(c) 1 â†’ D, 2 â†’ A, 3 â†’ C, 4 â†’ B
(d) 1 â†’ B, 2 â†’ C, 3 â†’ D, 4 â†’ A

Explaination: Properties of circle.

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 âˆ AOB = 100Â°, then âˆ BAT is equal to [Delhi 2011]

(a) 100Â°
(b) 40Â°
(c) 50Â°
(d) 90Â°

Explaination:
(c) âˆ AOB = 100Â°
âˆ OAB = âˆ OBA (âˆµ OA and OB are radii)
Now, in âˆ†AOB,
âˆ AOB + âˆ OAB + âˆ OBA = 180Â°
(Angle sum property of A)
â‡’ 100Â° + x + x = 180Â° [Let âˆ OAB = âˆ OBA = x]
â‡’ 2x = 180Â° â€“ 100Â°
â‡’ 2x = 80Â°
â‡’ x = 40Â°
Also, âˆ OAB + âˆ BAT = 90Â°
[âˆµ OA is radius and TA is tangent at A]
â‡’ 40Â° + ZBAT = 90Â°
â‡’ âˆ BAT = 50Â°

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