The incircle of \(\Delta ABC\) touches sides AB, BC and CA at points P, Q and R respectively. If AB = 12 cm, BC = 8 cm and CA = 10 cm, find AP, BQ and CR.

Doubtly Asked 29 Oct 2026 Practice test ssc 10th Save WhatsApp Report

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Answer: AP = 7 cm, BQ = 5 cm, CR = 3 cm

Tangent segments from an external point are congruent: let AP = AR = x, BP = BQ = y, CQ = CR = z.

AB: \(x + y = 12\); BC: \(y + z = 8\); CA: \(z + x = 10\).

Adding: \(2(x + y + z) = 30\) \(\therefore x + y + z = 15\).

\(\therefore x = 15 - 8 = 7\), \(y = 15 - 10 = 5\), \(z = 15 - 12 = 3\).

So AP = 7 cm, BQ = 5 cm, CR = 3 cm.

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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