Question

In ΔABC, show that $r_1.r_2.r_3 = r^{3}\ cot^{2}(\frac{A}{2})\ cot^{2}(\frac{B}{2})\ cot^{2}(\frac{C}{2})$.

Answer 1

Hi,

In this question, I have used the formulas for the circle related to the triangles.

This circle is called Escribed Circle.

It is also known as ex-circle or e-circle.

It is a type of circle, which touches one side of the triangle externally and two other extended sides internally.

Kindly see the Attachment.

I Hope it will help you.