Relating six properties of a triangle in one equation

Let a, b, and c be the sides of a triangle.

Let p be perimeter of the triangle.

Let r be the radius of the largest circle that can be inscribed in the triangle, and let R be the radius of the circle through the vertices of the triangle.

Then all six numbers can be related in one equation:

2prR = abc.

 

The post Relating six properties of a triangle in one equation first appeared on John D. Cook.