Area of triangle which inscribes in a circle

[Бк] , [Бй] , [^] , [Би]Area of triangle which inscribes in a circle / Measurement and conjecture(GC World : Various Problems ,MaxБEMin)

A, B, and C are on a circle O.
When will the area of ГвABC be maximized?
What idea does this figure have?

Forum of Geometric Constructor by Y.Iijima