# If E is a point o

Given in equilateral ΔABC, BE AC.

We know that in an equilateral triangle, the perpendicular from the vertex bisects the base.

CE = AE = AC/2

In ΔABE,

AB2 = BE2 + AE2

Since AB = BC = AC,

AB2 = BC2 = AC2 = BE2 + AE2

AB2 + BC2 + AC2 = 3BE2 + 3AE2

Since BE is an altitude,

BE = √3 AE

AB2 + BC2 + AC2

= 3BE2 + BE2

AB2 + BC2 + AC2 = 4BE2

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