In Δ ABC, seg AD is a median (D is the midpoint of side BC). If \(AB^2 + AC^2 = 122\) and BC = 10, find AD.

Q.2 (B)(2) In Δ ABC, seg AD is a median (D is the midpoint of side BC). If \(AB^2 + AC^2 = 122\) and BC = 10, find AD.

Doubtly AI Asked 27 Oct 2026 AI-generated · not yet verified ssc 10th Save WhatsApp Report

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Answer: AD = 6

D is the midpoint of BC, so BD = \(\dfrac{10}{2}\) = 5.

By Apollonius theorem, \(AB^2 + AC^2 = 2AD^2 + 2BD^2\).

\(122 = 2AD^2 + 2(5)^2 = 2AD^2 + 50 \Rightarrow 2AD^2 = 72 \Rightarrow AD^2 = 36 \Rightarrow AD = 6\).

Doubtly AI · 27 Oct 2026 AI-generated · not yet verified Report

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