An arbitrary triangle $ABC$ is given. Construct a line that divides it into two polygons, which have equal radii of the circumscribed circles.
(L. Blinkov)
As R= abc/4*area .Where a,b,c are sides of a triangle. now as the radii are equal we have that xyz/area1 = dcx/area2. where these are areas and sides of the newly formed triangles. now as they have the same altitude then area of their bases. so we have c/z = area1/area2=dc/yz so we get d=y and that means the triangle is an isosceles triangle.