Tangent Circles At Triangle Vertices

Question

I'm struggling to convert the formula from this article and translate it into Python, or any code for that matter, mainly because I find it hard to read math equations. Ideally, given the positions of A , B and C , find out the radii a' , b' and c' for the image on the left. Any help would be really apprciated.

Answer 1

If the vertex coordinates are (xa, ya) for point A , (xb, yb) for point B , and (xc, yc) for point C , you could use

a = math.sqrt((xb - xc)**2 + (yb - yc)**2)
b = math.sqrt((xa - xc)**2 + (ya - yc)**2)
c = math.sqrt((xb - xa)**2 + (yb - ya)**2)
ra = (b + c - a) / 2
rb = (c + a - b) / 2
rc = (a + b - c) / 2

and the desired radii are in ra, rb, rc . (I don't know how to translate a' etc. into Python so I used ra etc.) Values a, b, c are the lengths of the sides of the triangle. Note that I changed the formulas slightly from your linked article, to make them more symmetrical and pleasing to my eye.