MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 4

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section A, question 4, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q4 · 1 mark · MCQCircles

In the given figure, PQ is tangent to the circle with centre O. S is a point on the circle such that $∠ S QT = 5 5^{\circ}$ . The $m ∠ QP S$ is

(A) $5 5^{\circ}$
(B) $2 0^{\circ}$
(C) $3 5^{\circ}$
(D) $7 0^{\circ}$

Figure in the paper: A circle with centre O. P is outside the circle on the left; PQ is a tangent touching the circle at Q (upper left point of circle). PS is a secant/line from P through O to S, the point on the right of the circle diametrically opposite to the left end, so PS passes through the centre O. QT is a ray extended from Q beyond the tangent line to the upper right, with $∠ S QT = 5 5^{\circ}$ marked between chord QS and QT. Chord QS is drawn. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

Join OQ; what angle does it make with the tangent?

Hint 2

Triangle OQS is isosceles; then use angle sum in triangle PQS.

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.

$O Q ⊥ P T$ [tangent ⟂ radius], so $∠ O QS = 9 0^{\circ} - 5 5^{\circ} = 3 5^{\circ}$ . Since $O Q = O S$ , $∠ O S Q = 3 5^{\circ}$ .
In $△ P QS$ : $∠ P QS = 18 0^{\circ} - 5 5^{\circ} = 12 5^{\circ}$ , so $∠ QP S = 18 0^{\circ} - 12 5^{\circ} - 3 5^{\circ} = 2 0^{\circ}$ . Option (B).
1 mark

Answer: $2 0^{\circ}$ , option (B)

Where the marks are

Uses tangent ⟂ radius and isosceles triangle to get $∠ QP S = 2 0^{\circ}$ (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 30/5/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2026: question 4

Hints

Step-by-step solution

Revise the chapter

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