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The length of a… (Class 10 Maths Basic SQP 2023-24, Q23)

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

CBSE Class 10 Mathematics Basic 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

The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

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

Draw the radius to the point of contact. What angle does it make with the tangent?

Hint 2

The centre, the point of contact and A form a right triangle. Apply Pythagoras theorem with hypotenuse 5 cm.

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. Let O be the centre and AT the tangent, with T the point of contact. Then [tangent ⟂ radius]. By Pythagoras theorem, .

    ½ mark

  2. ½ mark

  3. cm, so the radius of the circle is 3 cm.

    1 mark

Answer: Radius = 3 cm

Where the marks are

  • Uses and writes (1/2 mark)
  • Substitutes to get (1/2 mark)
  • Radius = 3 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 2023-24 (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.