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In ∆ABC, point M is the midpoint of side BC. If, AB^{2 }+ AC^{2 }= 290 cm^{2}, AM = 8 cm, find BC.

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#### Solution

In ∆ABC, point M is the midpoint of side BC.

AB^{2} + AC^{2} = 2AM^{2} + 2BM^{2} ...[by Apollonius theorem]

290 = 2 (8)^{2} + 2BM^{2}

290 = 2 (64) + 2BM^{2}

290 = 128 + 2BM^{2}

2BM^{2} = 290 - 128

2BM^{2} = 162

BM^{2} = 81

BM = `sqrt81`

BM = 9 cm

Point M is the midpoint of BC

∴ BC = 2BM = 2 × 9

∴ BC = 18 cm.

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