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AB = BC = 10 cm. If AC = 7 cm… (Class 10 Maths 2023, Q8)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 8

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, section A, question 8, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q8 · 1 mark · MCQTriangles

In the given figure, cm. If cm, then the length of BP is :

  1. (A)3·5 cm
  2. (B)7 cm
  3. (C)6·5 cm
  4. (D)5 cm

Figure in the paper: Isosceles triangle ABC with apex B, AB = BC = 10 cm, base AC = 7 cm. A circle touches sides AB, BC and AC at P, Q and R respectively; P lies on AB, Q on BC, R on AC. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/5/1.

Hints

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

Hint 1

Tangents from one point to a circle are equal.

Hint 2

Since , R is the midpoint of AC.

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. Tangents from an external point are equal: , , . By symmetry cm, so cm.

  2. cm. Option (C).

    1 mark

Answer: 6·5 cm, option (C)

Where the marks are

  • Uses equal tangents to get , cm (1 mark)

Revise the chapter

  • Chapter: Triangles (notes, formulas, where marks are lost and every past question)
Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2023 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.