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(CP+CD)/PF wanted, touchpoints of incircle related

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

November 15, 2022
geometryincircle

Problem Statement

Let triangle ABCABC be a triangle right at BB. The inscribed circle is tangent to sides BC,CA,ABBC,CA,AB at points D,E,FD,E,F, respectively. Let CFCF intersect the circle at the point PP. If ∠APB=90∘\angle APB=90^{\circ}, find the value of CP+CDPF\dfrac{CP+CD}{PF}.
(tatari/nightmare)
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