Incircles and equal areas

[ins-]

Let $M, N, P$ are the tangent points of incircle with the sides of the triangle $ABC$ and $X, Y, Z$ are the tangent points of its excircles with the sides. Prove that $S_{MNP}=S_{XYZ}$.

[ins-]

It is a well known problem and can be proved in at least two ways. Don't loose your time.

[Edward_Tur]

$S_{MNP}=S_{XYZ}=\frac {r}{2R}S_{ABC}$.