Hey everyone, my friend found this math problem that he couldn't figure out and gave to me. I thought it was quite interesting. So far I haven't been able to find a way to get into it though. There's a circle, C1, with centre O and radius r. Point Y is anywhere outside the circle. Circle C3 has its centre at Y and its radius is OY. One of its points of intersection with C1 is P. Another circle, C2, with the same radius as C1, has its centre at P (and thus passes through O). A line passes through O and Y. C2 has another intersection with this line at X. Here is an image I made of the problem: The problem is twofold: 1. Let r = 1; find OX as OY equals 2, 3, and 4 (Find a general statement). 2. Let OY = 2; find OX as r = 2, 3, and 4 (Find a general statement). Basically you need to find the value of OX as r and OY change, and find a formula for it. Can anyone suggest anything? EDIT: I've figured out that triangles YOP and PXO are similar...maybe this will lead somewhere.