Triangles, Incircles, and an Excircle (Posted on 2014-05-24)
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 r1) touches side AB
at point I. The excircle of ΔACP (with radius r2) touches
side AC at point J.
(a) Prove that the line IJ cuts the perimeter of ΔABC
into two equal pieces.
(b) Prove that r1|CK| + r2|BK| is equal to the area of ΔABC.