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AX, AY and BC are… (Class 10 Maths Basic SQP 2026-27, Q27A)

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MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 27(A)

From the official CBSE sample question paper for 2026-27, section C, question 27(A), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27(A) · 3 marks · Short answerCircles

In the given figure, AX, AY and BC are tangents to the circle with P, R and Q respective point of contacts. Prove that

Figure in the paper: A circle with three tangents forming a triangle ABC. A is the external apex; two tangent lines AX and AY meet at A, with AX going down-left and AY going down-right. A third tangent BC touches the circle at Q, cutting across the top of the circle, with B on line AX and C on line AY. The points of contact on the circle are P (on AX), R (on AY) and Q (on BC). Labels: A at top, B and C near the top of the circle, X and Y at the ends of the tangent lines, P, Q and R on the circle. 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

Break side BC into two parts at the point of contact Q.

Hint 2

Replace each part by an equal tangent from B or C, then combine the segments along AX and AY.

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. Perimeter: [Q lies on BC]

    1 mark

  2. and [lengths of tangents from an external point to a circle are equal]

    So

    ½ mark

  3. (since B lies on AP and C lies on AR)

    [, tangents from A]

    1 mark

  4. Hence

    ½ mark

Answer: , proved

Where the marks are

  • Splits BC as BQ + QC in the perimeter (1 mark)
  • Uses BQ = BP and CQ = CR with the reason (½ mark)
  • Rewrites the perimeter as AP + AR = 2AP using AP = AR (1 mark)
  • Final conclusion (½ mark)

Revise the chapter

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.