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.
  

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