examday

/TMUA

In the diagram, line segments $AC$ and $DF$ are tangent to the circle at $B$ and $E$, respectively. $O$ is the centre of the circle, and radii are drawn to $B,P$, and $E$. Also, $AF$ intersects the circle at $P$ and $R$, and intersects $BE$ at $Q$, as shown.

If $\angle CAF=35^\circ$, $\angle DFA=30^\circ$, and $\angle FPE=25^\circ$, determine the angles $PEO$, $BOP$, and $BEP$ in degrees.