Lets call the radius of the hole "h", also lets call x and y the lengths of the center of the 45mm ball and 35mm until the center of the hole, such that these two segments form a straight line between eachother. (sorry if x and y definition is wierd, i'm unsure how else to say it) Now we notice that h^2 + x^2 =45^2 h^2 + y^2 = 35^2 x + y = 60 Substracting the first two we get x^2 - y^2 = (45+35)(45-35) => (x+y)(x-y) = 700 => x-y = 70/6 so x=70/6 + y Then 2y = 60 - 70/6 so y = 145/6 Then h^2 = (35+145/6)(35-146/6) so h is about 25.3 (I would have gotten it to a nicer expresion but AOPS won't let me annotate well since I'm new)