Question

A point D is on the side BC of an equilateral triangle ABC such that $\mathrm{DC}=\frac{1}{4}\mathrm{BC}$. Prove that AD² = 13 CD².

Answer 1

We are given ABC is an equilateral triangle with

We have to prove

Draw

In and we have

So by right side criterion of similarity we have

Thus we have

and

Since, therefore

We know that AB = BC = AC

We know that

Substitute in we get

Hence we have proved that