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In triangle ABC, line is a perpendicular bisector of BC. If BC = 12 cm, SM = 8 cm, find CS.

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Best answer

Given l1 is the perpendicular bisector of BC.

∴ ∠SMC = 90° and BM = MC

BC = 12 cm

⇒ BM + MC = 12 cm

MC + MC = 12 cm [∴ BM = MC]

2MC = 12

MC = 122

MC = 6 cm

Given SM = 8 cm

By Pythagoras theorem SC2 = SM2 + MC2

SC2 = 82 + 62

SC2 = 64 + 36

CS2 = 100

CS2 = 102

CS = 10 cm

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