Question:
Two given circles intersect at A and B. A straight line through B meets the circles again at C and D. Prove that CD is greatest when it is parallel to the line joining the centres
My attempt:
I made this diagram on Paint.NET:
Here CD is the required line parallel to the line $MNOP$ joining the centers N and O, and EF is another line not parallel to $MNOP$. Both CD and EF pass through point B. I know I have to prove that $CD > EF$.
But I don't know how to solve this problem. And I need hints.