Construct the triangle ABC given c, r and r', where c = |AB|, r is the radius of the inscribed circle, and r' is the radius of the other circle tangent to the segment AB and the lines BC and CA.
Solution
Put a = BC, b = CA, s = (a+b+c)/2 as usual. We have AX = s-a, AY = s-b (just chase around using the fact that the two tangents from a given point to a circle are equal). So XY = c. Thus mark the points X and Y a distance c apart. Then draw the two circles. Then draw the other common tangents, thus getting A, B and C.
© John Scholes
jscholes@kalva.demon.co.uk
29 Oct 2003
Last corrected/updated 29 Oct 03