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?
Best Answer
It seemed to me that since there are many different centers in a triangle, one of them might be useful for your construction. Going through the links of various centers, I stumbled upon a name for the problem you describe: these three circles are known as Malfatti circles.
The Wikipedia article has some details on a construction by Steiner. ℝⁿ was kind enough to add a comment below, providing links to details about some of the steps in that construction, namely the construction of bitangents and incircles to quadrilaterals. The latter seems obvious in hindsight…