Given three points on a circle, how should they be arranged to give the maximum area triangle?

manpreet Best Answer 2 years ago

I am trying to achieve multiple solutions to this problem using technology (i.e. Geometer's sketchpad) or perhaps alternatively solving without technology.

I am not sure if I am in the right direction in working on: - 3 unique points create a triangle - creating a bisection of each side - thus, a unique circumcentre = unique circum-radius - which creates a circle

Any guiding ideas would be appreciated

manpreet 2 years ago

Hint: Fix any two points and draw the chord ABAB. Now the area is maximised if the third point CC is farthest from ABAB, i.e. on the perpendicular bisector and when the triangle is isosceles.

As we can choose the first two points arbitrarily, the triangle has to be in fact equilateral.