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CBSE CLASS 10 · CHAPTER 10
Circles Assertion–Reason PYQs Class 10 CBSE (With Answers)
Practise 12 selected Circles Assertion–Reason questions from CBSE Class 10 previous-year board papers. Check each statement, then decide whether the Reason explains the Assertion. Two true statements do not always form a correct explanation.
12 distinct questions · 32 board-paper appearances Solutions prepared by Team TutorVertex · Reviewed: 25 October 2026
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Tangents, angles and cyclic quadrilaterals
Key results
The tangent at a point of a circle is perpendicular to the radius through that point.
The lengths of the two tangents drawn from the same external point are equal.
The perpendicular distance is the shortest distance from a point to a line.
Tangents at the two ends of a diameter are parallel.
If tangents PA and PB meet at P and the centre is O, then ∠APB + ∠AOB = 180°.
A quadrilateral with a pair of supplementary opposite angles is cyclic.
Question 1 · Basic + Standard
Assertion (A): A tangent to a circle is perpendicular to the radius through the point of contact.
Reason (R): The lengths of tangents drawn from an external point to a circle are equal.
Appeared in: 2023 · Basic; 2023 · Standard
Show Answer & Explanation
Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. By the radius–tangent theorem, the radius through the point of contact is perpendicular to the tangent.
Reason: True. The two tangent segments drawn from the same external point are equal.
Link: R states the equal-tangents theorem. It does not give the perpendicular relationship stated in A, so it does not explain A. Answer: B.
Question 2 · Standard
Assertion (A): Radius is the smallest distance of a tangent from the centre of the circle.
Reason (R): Radius is perpendicular to the tangent.
Appeared in: 2026 · Standard
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Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. Let the tangent touch the circle at A and let O be the centre. OA is the perpendicular distance from O to the tangent. The perpendicular is the shortest distance from a point to a line. Therefore the minimum distance is the radius OA.
Reason: True. The radius through the point of contact is perpendicular to the tangent.
Link: R identifies the perpendicular segment. Since a perpendicular gives the shortest distance, R explains A. Answer: A.
Question 3 · Standard
Assertion (A): A line drawn perpendicular to the tangent at point of contact passes through the centre of the circle.
Reason (R): Lengths of tangents drawn from an external point to a circle are equal.
Appeared in: 2025 · Standard
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Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. Let the tangent touch the circle at A and let O be its centre. OA is perpendicular to the tangent. Through A there is only one line perpendicular to that tangent. Hence the stated perpendicular is the line containing OA, and it passes through O.
Reason: True. Tangent segments from the same external point are equal.
Link: R concerns tangent lengths. It does not establish the perpendicular line through the centre, so it does not explain A. Answer: B.
Question 4 · Standard
Assertion (A): The tangents drawn at the end points of a diameter of the circle are parallel to each other.
Reason (R): The tangent to a circle is perpendicular to the radius at the point of contact.
Appeared in: 2023 · Standard · Supplementary examination
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Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. Let AB be a diameter. The tangent at A is perpendicular to AB. The tangent at B is also perpendicular to AB. Two lines perpendicular to the same line are parallel.
Reason: True. R states the radius–tangent theorem.
Link: Applying R at both ends of the diameter proves the parallelism in A. Answer: A.
Question 5 · Standard
Assertion (A): The tangents drawn at the end points of a diameter of a circle are parallel.
Reason (R): Diameter of a circle is the longest chord.
Appeared in: 2024 · Standard
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Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. Both tangents are perpendicular to the same diameter. Therefore they are parallel.
Reason: True. A chord cannot exceed the diameter in length. A diameter is itself a chord, so it is the longest chord.
Link: R compares chord lengths. It does not supply the perpendicular relationship needed to prove A. Answer: B.
Question 6 · Standard
Assertion (A): Tangents drawn at the end points of a diameter of a circle are always parallel to each other.
Reason (R): The lengths of tangents drawn to a circle from a point outside the circle are always equal.
Appeared in: 2025 · Standard
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Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. Both tangents are perpendicular to the diameter through their points of contact. Therefore they are parallel.
Reason: True. The two tangent segments from a single external point are equal.
Link: R concerns lengths from one external point. It does not explain why tangents at opposite ends of a diameter are parallel. Answer: B.
Question 7 · Basic
Assertion (A): If PA and PB are tangents drawn to a circle with centre O from an external point P, then the quadrilateral OAPB is cyclic.
Reason (R): In a cyclic quadrilateral, opposite angles are equal.
Question diagram redrawn from the official paper; not to scale.
Appeared in: 2024 · Basic
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Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. OA ⟂ PA and OB ⟂ PB. Thus ∠OAP = 90° and ∠OBP = 90°. These opposite angles of OAPB add to 180°. Hence OAPB is cyclic.
Reason: False as a general statement. Opposite angles of a cyclic quadrilateral are supplementary. They need not be equal.
Link: A follows from the two right angles. R incorrectly replaces supplementary angles with equal angles. Answer: C.
Question 8 · Standard
Assertion (A): If PA and PB are tangents drawn from an external point P to a circle with centre O, then the quadrilateral AOBP is cyclic.
Reason (R): The angle between two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.
Appeared in: 2023 · Standard
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Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. By R, ∠APB + ∠AOB = 180°. These are opposite angles of quadrilateral AOBP. Therefore AOBP is cyclic.
Reason: True. OA ⟂ PA and OB ⟂ PB. The angles of quadrilateral AOBP sum to 360°. Thus ∠APB + ∠AOB = 360° − 90° − 90° = 180°.
Link: R gives supplementary opposite angles, which is precisely the condition used to prove A. Answer: A.
Question 9 · Standard
Assertion (A): If two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre of the circle.
Reason (R): A parallelogram circumscribing a circle is a rhombus.
Appeared in: 2025 · Standard
Show Answer & Explanation
Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. Let PA and PB be the tangent segments, with centre O. In right triangles OAP and OBP, OP is common and OA = OB. Therefore △OAP ≅ △OBP by RHS. Hence ∠AOP = ∠BOP.
Reason: True. For a tangential quadrilateral ABCD, AB + CD = BC + AD. In a parallelogram, AB = CD and BC = AD. Thus 2AB = 2BC, giving AB = BC. All four sides are equal, so the parallelogram is a rhombus.
Link: R concerns a different figure. It does not explain the equality of the central angles in A. Answer: B.
Question 10 · Basic
Assertion (A): PA and PB are tangents to the circle centred at O and ∠OPA = 30°. Then △PAB is an equilateral triangle.
Reason (R): Lengths of tangents from an external point to a circle are equal in length.
Question diagram redrawn from the official paper; not to scale.
Appeared in: 2023 · Basic · Supplementary examination
Show Answer & Explanation
Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. By R, PA = PB. In △OAP and △OBP, OA = OB, OP is common and PA = PB. Therefore △OAP ≅ △OBP by SSS. Thus ∠OPB = ∠OPA = 30°. Hence ∠APB = 60°. Since PA = PB, ∠PAB = ∠PBA. Each equals (180° − 60°)/2 = 60°. Therefore △PAB is equilateral.
Reason: True. PA and PB are tangent segments from the same external point P, so PA = PB.
Link: R supplies the equal lengths used with the given 30° angle to establish all three 60° angles. R explains A. Answer: A.
CBSE uses the wording “explains Assertion completely / does not explain Assertion” in these papers. The displayed choices retain the same A–D meanings and order.
The displayed answer keys have been matched to official CBSE marking schemes. Explanations are written by Team TutorVertex using NCERT-style methods. Repeated questions are merged; all verified appearances and the original paper details are listed in the sources.