Problem

Source: Mathcenter Contest / Oly - Thai Forum 2010 (R1) p3 https://artofproblemsolving.com/community/c3196914_mathcenter_contes

Tags: geometry, incircle



Let triangle $ABC$ be a triangle right at $B$. The inscribed circle is tangent to sides $BC,CA,AB$ at points $D,E,F$, respectively. Let $CF$ intersect the circle at the point $P$. If $\angle APB=90^{\circ}$, find the value of $\dfrac{CP+CD}{PF}$. (tatari/nightmare)