TITLE: Construction of three tangent circles in a triangle
QUESTION [9 upvotes]: Given a triangle I want to construct three tangent circles inscribed in the triangle (every two sides of the triangle are tangent lines of one of the circles). For better understanding of the problem I tried to draw desired result (picture is only approximative, I do not know exact construction). Could you give me some hint, how exact construction can be done?

REPLY [4 votes]: I put a detail steps to show how to construct circles by straight and compass. the principle is provided by MvG.