# 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?

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Follow-up question: math.stackexchange.com/questions/266554/… –  user53153 Jan 4 '13 at 19:01

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 $$\frac{d}{2} \times \frac{1}{\tan\left(\frac{\alpha}{2}\right)}.$$