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PA is a common… (Class 10 Maths Basic SQP 2026-27, Q24)

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MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 24

From the official CBSE sample question paper for 2026-27, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerCircles

In the given figure, PA is a common tangent and QB and PC are the tangents from Q and P to the smaller and larger circle respectively. If QB = 5 cm and PC = 9 cm, then evaluate length of PQ.

Figure in the paper: Two circles with common centre O, the smaller inside the larger, touching at point A on the bottom. A straight line PA is a common tangent touching both circles at A (P lies to the right, on the line through A). Q lies on segment AP between A and P and is the point from which tangent QB touches the smaller circle at B (QB = 5 cm, labelled on the segment from Q to B). From P a tangent PC touches the larger circle at C (PC = 9 cm, labelled along the segment from C to P). The points C, B are on the upper part of the circles and the tangent lines CP and QB are drawn. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

Tangents drawn from an external point to a circle are equal in length.

Hint 2

QA and QB touch the same circle, and so do PA and PC. Then subtract along the line AP.

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.

  1. From Q, QA and QB are tangents to the smaller circle. [Lengths of tangents from an external point are equal], so cm.

    ½ mark

  2. From P, PA and PC are tangents to the larger circle. [Lengths of tangents from an external point are equal], so cm.

    ½ mark

  3. Q lies on AP, so cm.

    1 mark

Answer: PQ = 4 cm

Where the marks are

  • QA = QB = 5 cm with the equal-tangents reason (½ mark)
  • PA = PC = 9 cm (½ mark)
  • PQ = AP − AQ = 4 cm (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 paperSample paper 2026-27 (Basic): 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.