Locate the circle centre and draw lines from it to all 4 corners of the quadrilateral.
Since each resulting triangle has 2 sides of radius length, they are 4 isosceles triangles.
Now label equal angles at the circumference,
for example A, A, B, B, C, C, D, D.
Then (2A+2B)+(2C+2D)=360 degrees.
Also (A+D)+(B+C)=180 degrees.