A chord QR subtends an angle of 105° at the centre O of the circle. The measure of ∠RQP is (A) (75°)/(2) (B) (105°)/(2) (C) 75° (D) 15°

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2026: question 7

Set in the CBSE Class 10 board exam of 2026, paper 430/5/1, section A, question 7, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q7 · 1 mark · MCQCircles

A chord QR subtends an angle of $10 5^{\circ}$ at the centre O of the circle. The measure of $∠$ RQP is

(A) $\frac{7 5 ^{\circ}}{2}$
(B) $\frac{10 5 ^{\circ}}{2}$
(C) $7 5^{\circ}$
(D) $1 5^{\circ}$

Figure in the paper: A circle with centre O. A chord QR is drawn with Q and R on the circle; O is joined to Q and R forming the central angle. A ray from Q extends outward through point P, lying outside the circle, so that P, Q are on a line beyond Q away from the circle's interior. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

QP is a tangent; what angle does it make with OQ?

Hint 2

OQ = OR, so find the base angles of triangle OQR.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

QP is a tangent at Q, so $∠ O QP = 9 0^{\circ}$ [tangent ⟂ radius]. In isosceles $△ O QR$ , $∠ O QR = \frac{18 0 ^{\circ} - 10 5 ^{\circ}}{2} = 37. 5^{\circ}$ .
$∠ R QP = 9 0^{\circ} - 37. 5^{\circ} = 52. 5^{\circ} = \frac{10 5 ^{\circ}}{2}$ .
1 mark

Answer: $\frac{10 5 ^{\circ}}{2}$ , option (B)

Where the marks are

Uses tangent ⟂ radius and the isosceles triangle to get $10 5^{\circ} /2$ (1 mark)

Revise the chapter

Chapter: Circles (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Circles, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 7

Hints

Step-by-step solution

Revise the chapter

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