1. The distance between two parallel tangents of a circle of radius 4 cm is

(a) 2 cm

(b) 4 cm

(c) 6 cm

(d) 8 cm

Answer: d

Explanation:

Reason: Here radius, r = 4 cm

Required distance,

AB = OA + OB

= r + r = 2r = 2Ã—4 = 8 cm

2. In the given figure, if âˆ RPS = 25Â°, the value of âˆ ROS is

(a) 135Â°

(b) 145Â°

(c) 165Â°

(d) 155Â°

Answer: d

Explanation: 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

Answer: c

Explanation:

Reason: In right angle 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

Answer: a

Explanation: 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

Answer: a

Explanation: 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

Answer: b

Explanation:

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

Answer: a

Explanation: 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

Answer: c

Explanation:

Reason: In right angle Î”OAP, 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

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: b

Explanation: Reason: Since

BQ = BR â€¦(i) [âˆµ Tangents drawn from external points are equal]

CQ = CP â€¦[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

Answer: a

Explanation:

Reason: OPÂ² = OQÂ² + PQÂ²

169 = 25 + PQÂ²

PQÂ² = 144

PQ = 12

Area PQOR = ar (AOPQ) + ar (AOPR)

= 1/2 Ã— 12 Ã— 5 + 1/2 Ã— 12 Ã— 5 = 60 cmÂ²

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 [AI 2011]

(a) 40Â°

(b) 50Â°

(c) 140Â°

(d) 150Â°

Answer: c

Explanation:

(c) In quadrilateral ABOC

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

Answer: d

Explanation: (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

Answer: c

Explanation: (c) normal

14. 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°

Answer: a

Explanation:

(a) OP âŠ¥ PR [Y Tangent and radius are âŠ¥ to each other at the point of contact]

âˆ OPQ = 90Â° â€“ 50Â° = 40Â°

OP = OQ [Radii]

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°.

15. 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

Answer: c

Explanation:

16. 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: c

Explanation:

(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.

17. C (O, r_{1}) and C(O, r_{2}) are two concentric circles with r_{1} > r_{2} AB is a chord of C(O, r_{1}) touching C(O, r,_{2}) at C then

(a) AB = r_{1}

(b) AB = r_{2}

(c) AC = BC

(d) AB = r_{1} + r_{2}

Answer: c

Explanation:

(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

18. 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°

Answer: c

Explanation:

(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° + âˆ BAT = 90Â°

â‡’ âˆ BAT = 50Â°

19. In the figure PA and PB are tangents to the circle with centre O. If âˆ APB = 60Â°, then âˆ OAB is [Delhi 2011]

(a) 30Â°

(b) 60Â°

(c) 90Â°

(d) 15Â°

Answer: a

Explanation:

(a) Given âˆ APB = 60Â°

âˆµ âˆ APB + âˆ PAB + âˆ PBA = 180Â°

â‡’ APB + x + x = 180Â°

[âˆµ PA = PB âˆ´ âˆ PAB = âˆ PBA = x (say)]

â‡’ 60Â° + 2x = 180Â°

â‡’ 2x = 180Â° â€“ 60Â°

â‡’ 2x = 120Â°

â‡’ x = 120Â°/2 = 60Â°

Also, âˆ OAP = 90Â°

â‡’ âˆ OAB + âˆ PAB = 90Â°

â‡’ âˆ OAB + 60Â°= 90Â°

â‡’ âˆ OAB = 30Â°

20. In the given figure, TP and TQ are two tangents to a circle with centre O, such that âˆ POQ = 110Â°. Then âˆ PTQ is equal to [Foreign 2011]

(a) 55Â°

(b) 70Â°

(c) 110Â°

(d) 90Â°

Answer: b

Explanation:

(b) In quadrilateral POQT,

âˆ PTQ + âˆ TPO + âˆ TQO + âˆ POQ

= 360Â°

â‡’ âˆ PTQ + 90Â° + 90Â° + 110Â° = 360Â°

â‡’ âˆ PTQ + 290Â° = 360Â°

â‡’ âˆ PTQ = 360Â° â€“ 290Â° = 70Â°

21. In figure,PQ and PR are tangents to a circle with centre A. If âˆ QPA=27Â°, then âˆ QAR equals to [Foreign 2012]

(a) 63Â°

(b) 153Â°

(c) 110Â°

(d) 90Â°

Answer: c

Explanation:

(c) âˆ QPA = âˆ RPA

[âˆµ âˆ†AQP â‰… âˆ†ARP (RHS congruence rule)]

â‡’ âˆ RPA = 27Â°

âˆ´ âˆ QPR = âˆ QPA + âˆ RPA

= 27Â° + 27Â° = 54Â°

Now,

âˆ QAR + âˆ AQP + âˆ ARP + âˆ QPR = 360Â°

â‡’ âˆ QAR = 90Â° + 90Â° + 54Â° = 360Â°

â‡’ âˆ QAR = 360Â° â€“ 234Â° = 126Â°

22. In figure if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and âˆ BQR = 70Â°, then âˆ AQB is equal to [NCERT Exemplar Problems]

(a) 20Â°

(b) 40Â°

(c) 35Â°

(d) 45Â°

Answer:

Explanation:

(b) AB || PR

âˆ´ âˆ ABQ =âˆ BQR

[Alternate interior angles]

â‡’ âˆ ABQ = 70Â°

Also, âˆ BQR = âˆ BAQ [Angles in alternate segment]

â‡’ âˆ BAQ = 70Â°

In âˆ†AQB,

âˆ BAQ + âˆ ABQ + âˆ AQB = 180Â°

â‡’ 70Â° + 70Â° + âˆ AQB = 180Â°

â‡’ âˆ AQB = 180Â° â€“ 140Â° = 40Â°.

23. The common point of the tangent and the circle is called _____ .

Answer:

Explanation: point of contact

24. Two concentric circles are of radii 13 cm and 5 cm. The length of the chord of larger circle which touches the smaller circle is _____ .

Answer:

Explanation: 24 cm.

Hint: âˆµ AB touches the smaller circle

âˆ´ OC âŠ¥ AB and hence AC = BC

In right âˆ†OCA,

OAÂ² = OCÂ² + ACÂ²

â‡’ ACÂ² = 13Â² â€“ 5Â²

â‡’ AC = 12

âˆ´ AB = 2 Ã— 12 = 24 cm

25. A quadrilateral ABCD is drawn to circumscribe a circle. If AB =12 cm, BC = 15 cm and CD = 14 cm, then AD is equal to _____ .

Answer:

Explanation: 11 cm.

Hint: AB + CD = BC + AD

â‡’ 12+ 14= 15+ AD

â‡’ AD =11 cm.

26. Number of tangents to a circle which are parallel to a secant is ____ .

Answer:

Explanation: 2

27. A tangent PQ at a point P of a circle of radius 7 cm meets a line through centre O at a point Q so that OQ = 25 cm length PQ is ____ .

Answer: 24 cm

Explanation:

24 cm.

Hint: PQÂ² = OQÂ² â€“ OPÂ² = 252Â²- 7Â²

â‡’ PQ = 24 cm.

## Related Posts

## Category Lists (All Posts)

**Select Category**

All categories of this website are listed below with number of posts in each category for better navigation. Visitors can click on a particular category to see all posts related to that category.

- Biography of Scientists (1)
- Biology (65)
- Blog Posts (31)
- Career Guidance (1)
- CBSE Class 10 Maths (89)
- Assertion Reason Questions for Class 10 Maths (14)
- Case Study Questions for Class 10 Maths (15)
- Extra Questions for Class 10 Maths (12)
- Maths Formulas for Class 10 (1)
- MCQ Questions for Class 10 Maths (15)
- NCERT Solutions for Class 10 Maths (4)
- Quick Revision Notes for Class 10 Maths (14)
- RS Aggarwal Solutions for Class 10 Maths (12)

- CBSE Class 10 Science (185)
- Assertion Reason Questions for Class 10 Science (16)
- Case Study Questions for Class 10 Science (14)
- Evergreen Science Book Solutions for Class 10 (17)
- Extra Questions for Class 10 Science (21)
- HOTS for Class 10 Science (17)
- Important Questions for Class 10 Science (10)
- Lakhmir Singh Class 10 Biology Solutions (4)
- Lakhmir Singh Class 10 Chemistry Solutions (5)
- Lakhmir Singh Class 10 Physics Solutions (5)
- MCQ Questions for Class 10 Science (20)
- NCERT Exemplar Solutions for Class 10 Science (16)
- NCERT Solutions for Class 10 Science (15)
- Quick Revision Notes for Class 10 Science (4)
- Study Notes for Class 10 Science (17)

- CBSE Class 10 Social Science (21)
- CBSE CLASS 11 (1)
- CBSE Class 11 Chemistry (55)
- CBSE Class 11 Maths (54)
- CBSE Class 11 Physics (135)
- Assertion Reason Questions for Class 11 Physics (15)
- Case Study Questions for Class 11 Physics (12)
- Class 11 Physics Study Notes (5)
- Concept Based Notes for Class 11 Physics (2)
- Conceptual Questions for Class 11 Physics (10)
- Extra Questions for Class 11 Physics (9)
- MCQ Questions for Class 11 Physics (7)
- NCERT Solutions for Class 11 Physics (16)
- Physics Formulas for Class 11 (7)
- Revision Notes for Class 11 Physics (11)
- Very Short Answer Questions for Class 11 Physics (11)

- CBSE CLASS 12 (8)
- CBSE Class 12 Biology (27)
- CBSE Class 12 Business Studies (10)
- CBSE Class 12 Chemistry (82)
- Assertion Reason Questions for Class 12 Chemistry (15)
- Case Study Based Questions for Class 12 Chemistry (14)
- Extra Questions for Class 12 Chemistry (5)
- Important Questions for Class 12 Chemistry (15)
- MCQ Questions for Class 12 Chemistry (8)
- NCERT Solutions for Class 12 Chemistry (16)
- Revision Notes for Class 12 Chemistry (7)

- CBSE Class 12 Maths (50)
- CBSE Class 12 Physics (123)
- Assertion Reason Questions for Class 12 Physics (16)
- Case Study Based Questions for Class 12 Physics (14)
- Class 12 Physics Conceptual Questions (16)
- Class 12 Physics Discussion Questions (1)
- Class 12 Physics Latest Updates (1)
- Derivations for Class 12 Physics (6)
- Extra Questions for Class 12 Physics (4)
- Important Questions for Class 12 Physics (8)
- MCQ Questions for Class 12 Physics (14)
- NCERT Solutions for Class 12 Physics (18)
- Numerical Problems Based on Class 12 Physics (16)
- Revision Notes for Class 12 Physics (7)

- CBSE Class 6 Science (9)
- CBSE Class 7 (80)
- CBSE Class 8 Maths (6)
- CBSE Class 8 Science (17)
- CBSE Class 9 Maths (64)
- CBSE Class 9 Science (123)
- Assertion Reason Questions for Class 9 Science (16)
- Case Study Questions for Class 9 Science (14)
- Evergreen Science Book Solutions for Class 9 (15)
- Extra Questions for Class 9 Science (19)
- MCQ Questions for Class 9 Science (11)
- NCERT Solutions for Class 9 Science (15)
- Revision Notes for Class 9 Science (1)
- Study Notes for Class 9 Science (15)
- Topic wise MCQ Questions for Class 9 Science (2)
- Topicwise Questions and Answers for Class 9 Science (15)

- CBSE Class 9 Social Science (15)
- CHEMISTRY (8)
- Chemistry Articles (1)
- Daily Practice Problems (DPP) (3)
- H. C. Verma (Concepts of Physics) (18)
- ICSE Class 10 Biology (14)
- ICSE Class 10 Chemistry (5)
- ICSE Class 10 Maths (16)
- ICSE Class 10 Physics (12)
- ICSE Class 9 Maths (7)
- ICSE Class 9 Physics (10)
- IIT Foundation Mathematics (4)
- JEE Advanced Physics (3)
- JEE Chemistry (7)
- JEE Main Mock Test Series (1)
- JEE Mock Test Physics (1)
- JEE Study Material (1)
- JEE/NEET Physics (6)
- Latest Updates (9)
- CBSE Syllabus (1)

- Maths Articles (1)
- NCERT Books (3)
- NEET Chemistry (13)
- NEET Physics (55)
- NTSE (1)
- Physics (1)
- Physics Articles (13)
- Electrostatics (6)

- Physics for JEE Main (19)
- Previous Years Question Paper (3)
- Products (55)
- Products for CBSE Class 10 (13)
- Products for CBSE Class 11 (9)
- Products for CBSE Class 12 (6)
- Products for CBSE Class 7 (3)
- Products for CBSE Class 8 (1)
- Products for CBSE Class 9 (3)
- Products for Commerce (3)
- Products for Foundation Courses (2)
- Products for JEE Main & Advanced (10)
- Products for NEET (6)

- Question Answer (3)
- Topic Wise Study Notes (Physics) (2)
- Topicwise MCQs (2)
- Uncategorized (138)

**Test Series (Engineering, Medical and School Level Exams)**

Test series for students preparing for Engineering & Medical Entrance Exams are available. We also provide test series for School Level Exams. Tests for students studying in CBSE, ICSE or any state board are available here. Just click on the link and start test.