Question

If E is a point on the side CA of an equilateral triangle ABC, such that BE ⊥ CA, then AB² + BC² + CA² =

(a) 2 BE²

(b) 3 BE²

(c) 4 BE²

(d) 6 BE²

Answer 1

Correct option is (c) 4 BE²

Given: ABC is an equilateral triangle and BE ⊥ CA

Since, ABC is an equilateral triangle

So, E is the mid point of AC

Now, In △BEC

BE² + CE² = BC²

BE² + \(\left(\frac{BC}2\right)^2\) = BC²

BE² = \(\frac 34 \) BC²   ......(1)

Now, AB² + BC² + CA² = 3BC² ...... (2)

From (1) and (2), we get

AB² + BC² + CA² = 4BE²