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In triangle ABC, line I, is a perpendicular bisector of BC.

If BC = 12 cm, SM = 8 cm, find CS

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#### Solution

Given l_{1}, is the perpendicular bisector of BC.

∴ ∠SMC = 90°and BM = MC

BC = 12 cm

⇒ BM + MC = 12 cm

MC + MC = 12 cm

2MC = 12

MC = `12/2`

MC = 6 cm

Given SM = 8 cm

By Pythagoras theorem SC^{2} = SM^{2} + MC^{2}

SC^{2} = 8^{2} + 6^{2}

SC^{2} = 64 + 36

CS^{2} = 100

CS^{2} = 10^{2}

CS = 10 cm

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