# Seg AM is a median of ∆ ABC. If AB = 22, AC = 34, BC = 24, find AM

We know, By Apollonius theorem

In ΔABC, if M is the midpoint of side BC, then AB2 + AC2 = 2AM2 + 2BM 2

Given that,

AB = 22, AC = 34, BC = 24

AP is median i.e. P is the mid-point of BC

Putting values in equation

222 + 342 = 2AM2 + 2(12)2

484 + 1156 = 2AM2 + 288

1352 = 2AM2

AM2 = 676

AM = 26

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