In \(\Delta ABC\), \(\angle ACB = 90^\circ\), seg CD \(\perp\) side AB, A – D – B. If AD = 4 and DB = 9, find CD and AC.

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

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Answer: CD = 6, AC = \(2\sqrt{13}\)

By the theorem of geometric mean, \(CD^2 = AD \times DB = 4 \times 9 = 36\) \(\therefore CD = 6\).

In right-angled \(\Delta ADC\): \(AC^2 = AD^2 + CD^2 = 16 + 36 = 52\) \(\therefore AC = \sqrt{52} = 2\sqrt{13}\).

(Check with \(AC^2 = AD \times AB = 4 \times 13 = 52\).)

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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