MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 29(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section C, question 29(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(a) · 3 marks · Short answerCoordinate Geometry

A circle centred at (2, 1) passes through the points A(5, 6) and B(–3, K). Find the value(s) of K. Hence find length of chord AB.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

Both A and B are at a distance of one radius from the centre.

Hint 2

Equate $O A^{2}$ and $O B^{2}$ and solve for K; you get two values.

Hint 3

Find AB separately for each value of K.

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.

Let O(2, 1) be the centre. Radii are equal, so $O A = O B$ : $(5 - 2)^{2} + (6 - 1)^{2} = (- 3 - 2)^{2} + (K - 1)^{2} \Rightarrow 9 + 25 = 25 + (K - 1)^{2}$
1 mark
$(K - 1)^{2} = 9 \Rightarrow K - 1 = \pm 3 \Rightarrow K = 4$ or $K = - 2$
1 mark
For $K = - 2$ , B(–3, –2): $A B = (- 3 - 5)^{2} + (- 2 - 6)^{2} = 64 + 64 = 128 = 82$ units
½ mark
For $K = 4$ , B(–3, 4): $A B = (- 3 - 5)^{2} + (4 - 6)^{2} = 64 + 4 = 68 = 217$ units
½ mark

Answer: $K = 4$ or $K = - 2$ ; AB $= 217$ units (K = 4) or $82$ units (K = –2)

Where the marks are

Uses OA = OB with the distance formula (1 mark)
Finds $K = - 2, 4$ (1 mark)
AB $= 82$ for $K = - 2$ (½ mark)
AB $= 217$ for $K = 4$ (½ mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Applications of the Distance Formula

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/5/1 (Standard): 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 Standard 2026: question 29(a)

Hints

Step-by-step solution

Revise the chapter

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