Question 175
Let $\triangle ABC$ be given with $R$ radius of its circumcircle. Let $AB = c$, $BC = a$ and $CA = b$. Let $K_1$ and $K_2$ be the circles which pass through $C$ and are tangent to $AB$ at $A$ and $B$ respectively. Let $K$ be the circle of radius $r$ which is externally tangent to $K_1$, $K_2$ and tangent to the line $AB$.
a. Express $r$ in terms of $a, b, c$ and $R$.
b. Suppose $r = \frac{R}{4}$. Find $\angle C$.
a. Express $r$ in terms of $a, b, c$ and $R$.
b. Suppose $r = \frac{R}{4}$. Find $\angle C$.