MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 28

From the official CBSE sample question paper for 2025-26, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerCircles

A quadrilateral ABCD is drawn to circumscribe a circle, as shown in the given figure. Show that $\frac{A B + C D}{A D + B C} = 1$

Figure in the paper: Quadrilateral ABCD circumscribing a circle. Vertices: D top-left, C top-right, B bottom-right, A bottom-left. The circle touches the sides at R (on DC), Q (on CB), P (on AB) and S (on AD). See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Each vertex is an external point from which two tangents touch the circle.

Hint 2

Pair up equal tangent lengths at A, B, C, D and add them so that full sides appear.

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.

Lengths of tangents drawn from an external point to a circle are equal. So $A P = A S$ , $B P = B Q$ , $C R = C Q$ , $D R = D S$ .
1½ marks
Adding: $(A P + P B) + (C R + R D) = (A S + B Q) + (C Q + D S) = (A S + D S) + (B Q + C Q)$ , i.e. $A B + C D = A D + B C$ .
1 mark
Hence $\frac{A B + C D}{A D + B C} = 1$ .
½ mark

Answer: $A B + C D = A D + B C$ , so $\frac{A B + C D}{A D + B C} = 1$ .

Where the marks are

Writes the four pairs of equal tangents with reason (1½ marks)
Adds to obtain $A B + C D = A D + B C$ (1 mark)
Concludes the ratio equals 1 (½ mark)

Revise the chapter

Chapter: Circles (notes, formulas, where marks are lost and every past question)
Topic: Lengths of Tangents from an External Point

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 2025-26 (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.

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 28

Hints

Step-by-step solution

Revise the chapter

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