+130077 We can use the intersecting chord theorem
Let r be the radius
Let BP = r + 5
Let AP = r - 5
Let PC = sqrt (r^2 + 5)
So
PQ * PC = BP * AP
2sqrt [ r^2 +5^2 ] = (r + 5) (r -5)
2sqrt [ r^2 + 5^2 ] = r^2 - 25 square both sides
4 [ r^2 + 5^2 ] = r^4 - 50r^2 + 625
4r^2 + 100 = r^4 - 50r^2 + 625
r^4 - 54r^2 + 525 = 0 complete the square on r
r^4 - 54r^2 + 729 = -525 + 729
(r^2 - 27)^2 = 204 take the square root of both sides
r^2 - 27 = sqrt (204)
r^2= sqrt (204) + 27
r = sqrt [ 2sqrt 51) + 27 ] ≈ 6.43
