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Answer 1

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In an equilateral triangle ABC, D is a point on side BC such that 4BD = BC. Prove that 16AD

2

= 13 BC

2

.

Medium

Solution

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ABC is an equilateral triangle in which BD=

4

BC

Drawn AE perpendicular to BC

Since AE is perpendicular to BC then BE=EC=

2

BC

[In equilateral triangle perpendicular drawn from vertex to base bisects the base]

In △AED

AD²=AE

Putting the value of AE

2

from (2) in (1), we get

[As △ABC is an equilateral triangle]