Question

Let O be the center of the circle Γ, and P be a point outside of circle Γ. PA is tangential to Γ at A, and PO intersects Γ at D. If PD=14 and PA=42, what is the radius of Γ.

Answer 1

In this case the secant - tangent theorem says

PA^2 = PD x PC , where D in on the extension of PO as it hits the circle , making CD a diameter
Let the diameter be 2x , (radius = x)
(14)(2x+14) = 42^2
28x + 196 = 1764
28x = 1568
x = 56