MathsCBSE Class 10 · Basic · Sample paper, session 2024-25 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 22

From the official CBSE sample question paper for 2024-25, section B, question 22, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 2 marks · Very short answerCircles

In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm, then find the radius of the smaller circle.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

The radius of the smaller circle drawn to the point of contact is perpendicular to the chord.

Hint 2

A perpendicular from the centre bisects a chord. Then use Pythagoras in triangle $O M A$ .

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.

Figure: two concentric circles with centre $O$ . Chord $A B$ of the larger circle touches the smaller circle at $M$ . Join $O A$ and $O M$ .
$O M ⊥ A B$ [tangent ⟂ radius at the point of contact].
½ mark
The perpendicular from the centre bisects the chord, so $A M = \frac{8}{2} = 4$ cm.
½ mark
In right $△ O M A$ : $O M = O A^{2} - A M^{2} = 5^{2} - 4^{2} = 9 = 3$ cm.
So the radius of the smaller circle is 3 cm.
1 mark

Answer: 3 cm

Where the marks are

Correct figure with $O M ⊥ A B$ (½ mark)
$A M = 4$ cm (½ mark)
$O M = 25 - 16 = 3$ cm (1 mark)

Revise the chapter

Chapter: Circles (notes, formulas, where marks are lost and every past question)
Topic: Tangent Perpendicular to Radius Theorem

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 2024-25 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2024-25: question 22

Hints

Step-by-step solution

Revise the chapter

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