Finding intersecting points of a circle inside a triangle If I have a triangle, and I wanted to place a circle with a given diameter that fits snuggly inside any one of the three angles, how can I find the x, y points of where the triangle and circle meet? 

As a hint:  if the diameter is $d$ and the angle at a specific vertex is $\alpha$ then the distances from that vertex along each side is $$ \frac{d}{2} \times \frac{1}{\tan\left(\frac{\alpha}{2}\right)}.$$  

