>>1528340you can do it also with a little algebraic geometry (I did rotate the image so the coordinates may seem in the wrong order).
Consider the triangle ABC with side AC on the x-axis.
Set C=(0,0), then B=(4,5) and A= (14,0).
A vector perpendicular to CB = (4,5) is (5,-4), so the side bisector of CB has the equation (x,y) = (2,2.5) + k(5,-4). The side bisector of AC is simply the line (7,y). They intersect at the point D:
2 + 5k = 7
2.5 - 4k = y
so k = 1 and D = (7, -1.5).
The radius is simply the length of say
CD = ||(7,-1.5)|| = sqrt(7^2 + 1.5^2) = sqrt(205)/2.
