Question:

In ABC seg AP is a median. If BC = 18, AB2 + AC2 = 260 Find AP.

Answer:

Given AP is the median.
PC = BC/2
PC = 18/2 =9
AB2+AC2 = 2AP2+2PC2 [Apollonius theorem]
260 = 2AP2+2×92
2AP2 = 260-2×92
2AP2 = 260-162
AP2 = 68/2 = 49
Taking square roots on both sides
AP = 7
Hence AP = 7 units.

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