In the triangle $ABC$ with sides $AC = b$ and $AB = c$, the extension of the bisector of angle $A$ intersects it's circumcircle at point with $W$. Circle $\omega$ with center at $W$ and radius $WA$ intersects lines $AC$ and $AB$ at points $D$ and $F$, respectively. Calculate the lengths of segments $CD$ and $BF$. (Evgeny Svistunov)
Problem
Source: 2023 Yasinsky Geometry Olympiad VIII-IX basic p6 , Ukraine
Tags: geometry, circles, circumcircle
