we know the lines are angle bisectors, so the line makes twin angles, so the line FP is making twin angles, we also know the angle FZP and the angle FYP are right-angles, as well as FP is a common hypotenuse to two right triangles, thus by the HA postulate for right triangles, triangleFPZ and triangle FPYare both congruent, so their sides are also congruents, thus PY = PZ.