Question

In ΔABC, show that $(r_1 + r_2)tan\frac{C}{2} = (r_3 - r)cot\frac{C}{2} = c$.

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.

Its center is called ex-center.

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.