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The length of a tangent… (Class 10 Maths Basic 2024, Q24)

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MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2024: question 24

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerCircles

The length of a tangent drawn to a circle from a point A, at a distance of 10 cm from the centre of the circle, is 6 cm. Find the radius of the circle.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/5/1.

Hints

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

Hint 1

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

Hint 2

The distance from A to the centre is the hypotenuse of a right triangle.

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 at T. Then [tangent ⟂ radius at point of contact], so in right , by Pythagoras theorem:

    1 mark

  2. cm

    1 mark

Answer: Radius = 8 cm

Where the marks are

  • Uses radius ⟂ tangent and Pythagoras: (1 mark)
  • Gets 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 paper2024 board paper, set 430/5/1 (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.