Let the two legs of the triangle be length x and y. We see that h=x+y-2r.
Draw three "sub-triangles" by connecting the center of the circle to the vertices of the triangle.
The area of the triangle is the sum of the areas of the 3 smaller triangles. Thus the area is xr/2+yr/2 + hr/2 = r(x+y+h)/2 = r(h+2r+h)/2 = r(h+r).
The area of the circle is πr2, so the ratio of areas is (π r2)/r(h+r) = π r/(h+r).