THE REMARKABLE INCIRCLE OF A TRIANGLE.

The article discusses several unusual facts regarding triangles of which are related to properties of the incircle. The proof of these facts integrate the use of geometry, algebra and trigonometry. It shows that the inradius of a Pythagorean triangle is an integer. It demonstrates that the incircle provides a simple geometric meaning for the factors that occur under this radical. Finally, it presents how to find non-right triangles with integer sides and integer inradius. Through the results, several connections are made between the classical subjects of geometry and number theory.