prove that triangle of maximum area inscribed in a cicle is equilateral triangle

If an equilateral triangle has to be inscribed in the circle, it will comprise of 3 chords. or one can say that the circle gets divided in three sectors.the central angle  for each sector which we get by dividing the central angle is 120 degrees. Equal chords subtend equal angles at the centre. therefore if all three central angles have to be equal all three chords are equal,forming an equilateral triangle.