I have a convex quadrilateral defined (in counterclockwise order) by the points $$p_0=(x_0,y_0)\\p_1=(x_1,y_1)\\p_2=(x_2,y_2)\\p_3=(x_3,y_3)$$ I want to found the minimum radius between all the radius of circles tangent to 3 edges. In the image below, it's radius r4
(more info here)
At the moment, I'm thinking of calculating the bisectors, find the point of intersection and projecting that onto an edge and then be able to find the radius... but I'm really not able to find an efficient way to do it.
HINT.
You can compare the sums of opposite sides of your quadrilateral ($p_0p_1+p_2p_3$ and $p_0p_3+p_1p_2$): the two sides with the greater sum are both touched by the minimum circle. The center of the circle must then belong to the bisector of those two sides.