A line through vertex A of ΔABC intersects line BC

at point P such that B lies between P and C. The incircle

of ΔABC (with radius r) touches side BC at point K.

The incircle of ΔABP (with radius r

_{1}) touches side AB

at point I. The excircle of ΔACP (with radius r

_{2}) touches

side AC at point J.

(a) Prove that the line IJ cuts the perimeter of ΔABC

into two equal pieces.

(b) Prove that r

_{1}|CK| + r

_{2}|BK| is equal to the area of ΔABC.