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Question
In ΔABC, seg AP is a median. If BC = 18, AB2 + AC2 = 260, then find the length of AP.
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Solution
We know, By Apollonius theorem
In ΔABC,
if P is the midpoint of side BC, then AB2 + AC2 = 2AP2 + 2BP 2
Given that, AP is median i.e. P is the mid-point of BC
BP = CP = `1/2"BC" = 9`
And BC = 18 cm
and AB2 + AC2 = 260
⇒ 260 = 2AP2 + 2(9)2
⇒ 260 = 2AP2 + 162
⇒ 98 = 2AP2
⇒ AP2 = 49
⇒ AP = 7 units
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