CBSE Class 10 Mathematics Circles MCQs Set 12

Mathematics Objective Questions and Answers: Chapter 10 Circles

Access targeted multiple-choice questions for Chapter 10 Circles designed to align with the latest CBSE academic syllabus for Class 10 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Download Chapter 10 Circles MCQs with Answers

View or download the dedicated Chapter 10 Circles MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions

Question 1: PA and PB are tangents from P to a circle with centre C. If ∠APB = 40°, then ∠ACB is equal to
(a) 100°
(b) 140°
(c) 50°
(d) 70°
Show Answer & Explanation

Answer: (b) 140°

Explanation:
1. ∠CAP = ∠CBP = 90° (radius ⊥ tangent).
2. In quadrilateral ACBP: ∠ACB = 360° − 90° − 90° − 40° = 140°.

Teacher's Note:
1. The angle between the tangents and the angle at the centre are supplementary.
2. 140° + 40° = 180°.

Question 2: PA and PB are tangents from P to a circle with centre O. If ∠AOB = 130°, then ∠APB is equal to
(a) 50°
(b) 65°
(c) 130°
(d) 40°
Show Answer & Explanation

Answer: (a) 50°

Explanation:
1. ∠OAP = ∠OBP = 90°.
2. ∠APB = 360° − 90° − 90° − 130° = 50°.

Teacher's Note:
1. Angle at the centre + angle between tangents = 180°.
2. Use the angle sum of quadrilateral OAPB.

Question 3: PT is a tangent to a circle with centre O. If PT = 12 cm and PO = 13 cm, the radius of the circle is
(a) 6 cm
(b) \( \sqrt{313} \) cm
(c) 1 cm
(d) 5 cm
Show Answer & Explanation

Answer: (d) 5 cm

Explanation:
1. OT ⊥ PT, so OT² = PO² − PT² = 169 − 144 = 25.
2. OT = 5 cm.

Teacher's Note:
1. The 5-12-13 triple appears often.
2. Radius ⊥ tangent gives the right angle.

Question 4: PT is a tangent at T to a circle with centre O. If the radius is 8 cm and PT = 15 cm, then OP is
(a) 23 cm
(b) \( \sqrt{161} \) cm
(c) 17 cm
(d) 12 cm
Show Answer & Explanation

Answer: (c) 17 cm

Explanation:
1. OP² = OT² + PT² = 64 + 225 = 289.
2. OP = 17 cm.

Teacher's Note:
1. The 8-15-17 triple.
2. The hypotenuse is OP.

Question 5: O is the centre of a circle of radius 6 cm and B is a point such that OB = 10 cm. The length of the tangent AB drawn from B (A on the circle) is
(a) 4 cm
(b) 8 cm
(c) \( \sqrt{136} \) cm
(d) 16 cm
Show Answer & Explanation

Answer: (b) 8 cm

Explanation:
1. ∠OAB = 90°, so AB² = OB² − OA² = 100 − 36 = 64.
2. AB = 8 cm.

Teacher's Note:
1. A tangent is perpendicular to the radius at the point of contact.
2. The 6-8-10 triangle.

Question 6: PA is a tangent at A to a circle with centre O, and AB is a diameter. If ∠POB = 115°, then ∠APO is equal to
(a) 25°
(b) 65°
(c) 35°
(d) 90°
Show Answer & Explanation

Answer: (a) 25°

Explanation:
1. ∠PAO = 90°, and ∠POB is an exterior angle of triangle APO.
2. ∠APO + ∠PAO = ∠POB, so ∠APO = 115° − 90° = 25°.

Teacher's Note:
1. An exterior angle equals the sum of the two opposite interior angles.
2. Check: ∠AOP = 65° and 65° + 25° + 90° = 180°.

Question 7: PA and PB are tangents from P to a circle with centre O. If ∠APB = 60°, then ∠AOB is
(a) 60°
(b) 90°
(c) 30°
(d) 120°
Show Answer & Explanation

Answer: (d) 120°

Explanation:
1. ∠OAP = ∠OBP = 90°.
2. ∠AOB = 360° − 90° − 90° − 60° = 120°.

Teacher's Note:
1. The angle at the centre and the angle between the tangents are supplementary.
2. 120° + 60° = 180°.

Question 8: CP and CQ are tangents to a circle with centre O, and ARB is another tangent touching the circle at R, with A on CP and B on CQ. If QC = 11 cm and BC = 7 cm, then BR equals
(a) 7 cm
(b) 11 cm
(c) 4 cm
(d) 18 cm
Show Answer & Explanation

Answer: (c) 4 cm

Explanation:
1. Tangents from B: BR = BQ.
2. BQ = QC − BC = 11 − 7 = 4 cm, so BR = 4 cm.

Teacher's Note:
1. Tangents from an external point are equal.
2. Q lies between B and C on line CQ.

Question 9: Triangle ABC circumscribes a circle that touches AB at R, AC at Q and BC at P. If AR = 4 cm, BR = 3 cm and AC = 11 cm, then BC is
(a) 7 cm
(b) 10 cm
(c) 14 cm
(d) 12 cm
Show Answer & Explanation

Answer: (b) 10 cm

Explanation:
1. AQ = AR = 4 cm, so CQ = 11 − 4 = 7 cm.
2. CP = CQ = 7 cm and BP = BR = 3 cm.
3. BC = BP + PC = 10 cm.

Teacher's Note:
1. Name the equal tangent pairs from each vertex.
2. The perimeter is 4 + 3 + 3 + 7 + 7 + 4 = 28 cm.

Question 10: TA and TB are tangents from T to a circle with centre O. If ∠ATO = 40°, then ∠AOB is
(a) 100°
(b) 80°
(c) 50°
(d) 130°
Show Answer & Explanation

Answer: (a) 100°

Explanation:
1. OT bisects ∠ATB, so ∠ATB = 80°.
2. ∠AOB = 180° − 80° = 100°. (Or ∠AOT = 50° and ∠AOB = 2 × 50°.)

Teacher's Note:
1. OT bisects both the angle at T and the angle at O.
2. Triangle OAT has angles 90°, 40° and 50°.

Question 11: The length of the tangent from a point P to a circle is 15 cm and P is 17 cm from the centre. The radius of the circle is
(a) 2 cm
(b) 16 cm
(c) \( \sqrt{514} \) cm
(d) 8 cm
Show Answer & Explanation

Answer: (d) 8 cm

Explanation:
1. r² = 17² − 15² = 289 − 225 = 64.
2. r = 8 cm.

Teacher's Note:
1. Radius ⊥ tangent makes a right triangle with hypotenuse OP.
2. Use a² − b² = (a − b)(a + b).

Question 12: The two tangents from an external point P to a circle with centre O are PA and PB. If ∠APB = 70°, then ∠AOB is
(a) 70°
(b) 100°
(c) 110°
(d) 120°
Show Answer & Explanation

Answer: (c) 110°

Explanation:
1. ∠OAP = ∠OBP = 90°.
2. ∠AOB = 360° − 90° − 90° − 70° = 110°.

Teacher's Note:
1. Quadrilateral OAPB has two right angles.
2. ∠AOB and ∠APB are supplementary.

Question 13: A chord of the larger of two concentric circles touches the smaller circle. If the chord is 8 cm long and the diameter of the smaller circle is 6 cm, the diameter of the larger circle is
(a) 5 cm
(b) 10 cm
(c) 14 cm
(d) 12 cm
Show Answer & Explanation

Answer: (b) 10 cm

Explanation:
1. The radius of the smaller circle is 3 cm, and half the chord is 4 cm.
2. R² = 3² + 4² = 25, so R = 5 cm and the diameter is 10 cm.

Teacher's Note:
1. The radius to the touching point bisects the chord.
2. Remember to double the radius at the end.

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FAQs

Where can I access latest CBSE Class 10 Mathematics Circles MCQs Set 12?

You can get most exhaustive CBSE Class 10 Mathematics Circles MCQs Set 12 for free on StudiesToday.com. These MCQs for Class 10 Mathematics are updated for the 2026-27 academic session as per CBSE examination standards.

Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics Class 10 material?

Yes, our CBSE Class 10 Mathematics Circles MCQs Set 12 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

How do practicing Mathematics MCQs help in scoring full marks in Class 10 exams?

By solving our CBSE Class 10 Mathematics Circles MCQs Set 12, Class 10 students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the Mathematics.

Do you provide answers and explanations for CBSE Class 10 Mathematics Circles MCQs Set 12?

Yes, Mathematics MCQs for Class 10 have answer key and brief explanations to help students understand logic behind the correct option as its important for 2026 competency-focused CBSE exams.

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