Circle with center O. AB is a diameter, CO is perpendicular to AB. PO = 25 and PQ = 8. Find the radius.
+129899 By the intersecting chord theorem
PQ * CP = PB * AP
PB = r + 25
AP = r -25
So
8 * CP = (r + 25) (r -25)
CP = (r^2 -625) / 8 → CP^2 = (r^2 -625)^2 / 64
Therefore
CP^2 - PO^2 = CO^2 = r^2
(r^2 - 625)^2 /64 - 25^2 = r^2
r^4 - 1250r^2 + 390625 - 40000 = 64r^2
r^4 - 1314r^2 + 350625 = 0
Solving this produces that the possible positive values for r ≈ 19.296 or r ≈ 30.686
r must be > 25 ....so....r ≈ 30.686
