Question 144
The following figure shows a triangle $ABC$ with sides $AB=13~\mathrm{cm}$, $BC=14~\mathrm{cm}$ and $CA=15~\mathrm{cm}$. The center circumference $I$ is tangent to the sides $AB$, $BC$ and $CA$ at points $F$, $D$ and $E$, respectively. Points $R$, $S$, $T$, $U$, $V$ and $X$ are marked in Extensions of the sides of the triangle $ABC$ such that $AR=AS=14~\mathrm{cm}$, $BT=BU=15~\mathrm{cm}$ and $CV=CX=13~\mathrm{cm}$. 
(a) Prove that $AE=AF$.
(b) Determine the measure of segment $BF$.
(c) Prove that the hexagon $RSTUVX$ is inscribable, that is, show that there is a circle passing through its six vertices.
(a) Prove that $AE=AF$.
(b) Determine the measure of segment $BF$.
(c) Prove that the hexagon $RSTUVX$ is inscribable, that is, show that there is a circle passing through its six vertices.