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In Delta ABC, seg AP is a median. If BC ...

In `Delta ABC`, seg AP is a median. If BC = 18, `AB^(2) + AC^(2) = 260` then find the length of AP.

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The correct Answer is:
Length of median AP is 7

In `Delta ABC`, seg, AP is a medium
`:. BP = PC = (1)/(2) xx BC` ….(P is the midpoint of sedg BC)
`= ((1)/(2) xx 18)`
`:. BP = PC = 9`
By Apollonius theorem,
`AB^(2) + AC^(2) = 2 AP^(2) + 2BP^(2)`
`:. 260 = 2AP^(2) + 2(9)^(2)`
`:. 260 = 2AP^(2) + 162`
`:. 2AP^(2) = 260 - 162`
`:. 2AP^(2) = 98`
`:. AP^(2) = (98)/(2)`
`:. AP^(2) = 49`
`:. AP = 7` (Taking square roots of both the sides
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