Inscribing Four Circles in a Triangle

Inscribe a circle in a triangle ABC; let denote rM its radius.
Construct tangents to the inscribed circle parallel to the sides of the triangle.
Construct inscribed circles within each of the smaller triangles with radii rA, rB, and rC.
Then rA + rB + rC = rM.

rA rB rC
rM rA+rB+rC