In \(\Delta ABC\), seg AD bisects \(\angle BAC\) and D lies on side BC. If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.

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

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Answer: BD = 2.5 cm, DC = 3.5 cm

By the angle bisector theorem, \(\dfrac{BD}{DC} = \dfrac{AB}{AC} = \dfrac{10}{14} = \dfrac{5}{7}\).

Let BD = 5k and DC = 7k. Then BD + DC = BC gives \(12k = 6\) \(\therefore k = 0.5\).

\(\therefore BD = 5 \times 0.5 = 2.5\) cm and \(DC = 7 \times 0.5 = 3.5\) cm.

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

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