Question

AB = AC

PROVE THAT : AC^2 = 2BC . CD

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Answer 1

solution : In ∆ ADC

AC2 = AD2 + DC2

AC2 = AB2 - BD2 + DC2(AS ABD is a right angled triangle)

or AC2 = AB2 + DC2 - BD2

AC2 = AB2 + DC2 - ( DC-BC )2

or AC2 = AB2 + DC2 - (DC2 + BC 2 -2 DC. BC)

or AC2 = AB2 + DC2 - DC2 - BC 2 + 2 DC. BC

or AC2 = AB2 - AB 2 + 2 DC. BC (As AB = BC )

.'. AC2 = 2 DC. BC Proved

$\huge \boxed{hope \: it \: helps \: u}$