# ABC is an equilat

Given: AB = BC = CA = x

To prove: AB2 + BC2 + CA2 = 4AD2

Proof:

We know that in an equilateral triangle perpendicular from any vertex on opposite side bisects it.

So, BD = DC = 1/2BC ……………… (1)

By applying Pythagoras theorem in ΔABD, we get,

AB2 = AD2 + BD2 [ H2 = P2 + B2]

By substituting BD from eqn. (1) we get,

4AB2 - AB2 = 4AD2 [Given: AB = BC]

AB2 + BC2 + CA2 = 4AD2 [ AB = BC = CA]

Hence proved.

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