As seen in the attachment I have a 100 x 100 square and a quarter of a circle with radius being 104.032. This radius gives an area of 8500 from 1/4(104.032^2) * Pi

My problem is I need the shaded area to equal 8500. I have to do this while still using a circle radius. So I need to know how, in terms of formulas ect, to find the radius to make the shaded region equal 8500. Any help would be great.

I tried to set up a system of equations with splitting the area into two equal triangles and then a pie section. Areas being B*100 for the area sum of the triangles and (theta * R^2)/2 in radians for the area of the pie section. The sum of these would be set to 8500. Problem I ran into was I ended up with an equation that was unsolvable. I suspect there are easier ways of approaching this like maybe area under a curve or something. I appreciate any help, thank you for your time.