Answer :

Δ ABC is an equilateral triangle

By Pythagoras theorem in triangle ABD

AB2 = AD2 + BD2

but BD = 1/2 BC ( In a triangle, the perpendicular from the vertex to the base bisects the base)

thus AB2 = AD2 + {1/2 BC}2

AB2 = AD2 + 1/4 BC2

4 AB2 = 4AD2 + BC2

4 AB2 - BC2 = 4 AD2

(as AB = BC we can subtract them )

Thus 3AB2 = 4AD2

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