cyclic quadrilateral

Hint of oslving this one
take the triangle of these two sides and inclusive angle

the area is easily found..

also the area of the other triangle of this quadrilateral is known.

Now you also know the diagonal of this quadrilateral.

What you need to do is to draw the perpendicular bisector of this diagonal

Then you know the area on both sides will be equal

so you know the heights on both sides.

So you know the radius. (Sum of these heights)

Now you know the area

Triangles BCD and BWD have the same area

the red line is perpendicular to the diagonal (BC) of the quadrilateral ABCD

Thus we know the height of the red line on both sides

thus we know the length of the red line which happens to be the diagonal