This is a classic extremal problem. The often use a chessboard coloring.
A geometric inequality proof for an obtuse-angled triangle ABCcap A cap B cap C , requiring the solver to show that bmo 2008 solutions
In circle 1, angle between tangent at C and chord CA equals angle in opposite segment CBA. Similarly, in circle 2, angle between tangent at D and chord DA equals angle DBA. This is a classic extremal problem