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From an external point… (Class 10 Maths SQP 2023-24, Q23)

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MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 23

From the official CBSE sample question paper for 2023-24, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerCircles

From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At a point E on the circle, a tangent is drawn to intersect PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of PCD.

Figure in the paper: Circle with centre O. External point P with tangents PA (touching at A, upper) and PB (touching at B, lower). A third tangent touches the circle at E, meeting PA at C and PB at D; the triangle PCD is formed. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Tangents drawn from the same external point are equal.

Hint 2

Split CD into CE + ED and replace each part by an equal tangent.

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. , and [tangents from an external point are equal].

    ½ mark

  2. Perimeter of . Replacing CE by CA and ED by DB gives .

    1 mark

  3. Perimeter cm.

    ½ mark

Answer: 20 cm

Where the marks are

  • States the equal-tangent pairs (½ mark)
  • Rewrites the perimeter as PA + PB (1 mark)
  • Gets 20 cm (½ 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 2023-24 (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.