Geometry Stumper

[Thomas Puettmann]

In a university course on elementary geometry you gradually build up skills to solve these problems almost immediately.

Some things just flash when you read the problem.

Angular bisectors --> inscribed circle --> buy two, get one free

Now the only point is that the circle in question is not the inscribed circle of the triangle ABC, but the circle whose midpoint is D and which touches the three lines AB, AC, and BC.

Maybe some of you would like to give this approach a try.