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From a point P, the… (Class 10 Maths Basic 2023, Q25)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 25

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerCircles

From a point P, the length of the tangent to a circle is 24 cm and the distance of P from the centre of the circle is 25 cm. Find the radius of the circle.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

The radius to the point of contact is perpendicular to the tangent.

Hint 2

This makes a right triangle with hypotenuse 25 cm; use Pythagoras.

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. Figure: circle with centre O, external point P, tangent PQ touching the circle at Q, with cm, cm and OQ joined; [tangent ⟂ radius at point of contact].

    ½ mark

  2. In right , by Pythagoras theorem:

    1 mark

  3. cm, so the radius is 7 cm.

    ½ mark

Answer: Radius = 7 cm

Where the marks are

  • Correct figure with right angle at point of contact (½ mark)
  • Applies Pythagoras: (1 mark)
  • Radius = 7 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 paper2023 board paper, set 430/6/1 (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.