Question 142
Given a triangle of vertexes $A$, $B$ and $C$, and with sides of length $a = BC$, $b = AC$ and $c = AB$, let's call $D$ to the intersection point of the $AB$ side with the angle bisector $C$. Show that: $$
CD = \frac{2ab \cos \frac{C}{2}}{a + b}
$$
CD = \frac{2ab \cos \frac{C}{2}}{a + b}
$$