MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 24(a)

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section B, question 24(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(a) · 2 marks · Very short answerCircles

In the given figure, AP, AQ and BC are tangents to the circle with centre O. If $A B = 6$ cm, $A C = 7$ cm and $B C = 5$ cm, then what is the length of AP ?

Figure in the paper: A circle with centre O inside a triangle-like figure: apex A at top with tangent lines AP and AQ touching the circle at P (left) and Q (right); a third tangent BC touches the circle at R, with B on AP and C on AQ. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

Tangents drawn from an external point to a circle are equal in length.

Hint 2

Split AP as AB + BP and replace BP by BR; do similarly for AQ.

Hint 3

Add AP and AQ and notice BR + CR = BC.

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.

Tangents from an external point are equal: $B P = B R$ , $C Q = C R$ , $A P = A Q$ . So $A P = A B + B P = A B + B R$ and $A Q = A C + C Q = A C + C R$ .
½ mark
Adding: $A P + A Q = A B + A C + (B R + C R) = A B + A C + B C$
½ mark
Since $A P = A Q$ : $2 A P = 6 + 7 + 5 = 18$
½ mark
$\Rightarrow A P = 9$ cm
½ mark

Answer: AP = 9 cm

Where the marks are

Writes $A P = A B + B R$ and $A Q = A C + C R$ using equal tangents (½ mark)
Adds to get $A P + A Q = A B + B C + A C$ (½ mark)
$2 A P = 18$ (½ mark)
$A P = 9$ cm (½ mark)

Revise the chapter

Chapter: Circles (notes, formulas, where marks are lost and every past question)
Topic: Solving Problems Using Tangent Properties

Practise this chapterBoard-style questions from Circles, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 430/4/1 (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.

CBSE Class 10 Mathematics Basic 2026: question 24(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Circles