As you posted a file in Prime Express 4.0 format, I thought I would provide an Express solution as well. Basically simply two perpendicular bisectors are intersected to get the center M of the circle and the radius is the distance of M to one of the three circle points A, B or D.
Here a more basic approach without analytical geometry, just using good old Pythagoras.
The solving of a system of equations (in r and MF) is somewhat hidden by first expressing MF with r and putting that expression in the second equation.
"root" function can be avoided by some manual term manipulations
Since this was for fun I thought I'd see if I could replace Mathcad with Gemini Ai.
I have a circle. I draw a chord AB =45cm. Then I draw a line at 90 degrees to AB =20cm. This line is inside the circle. I draw another line perpendicular to AC towards the circumference. This line is CD =15cm and terminates on the circumference of the circle. Determine the radius.
The Baudhayana Shulba Sutra, an Indian text written between the 8th and 5th century BC, contains a statement of the theorem, a specific case for the isosceles right triangle, and the general case. This predates Pythagoras by about 300 years.
