a chord AB of a circle subtends an angle that is not equal to 60 degees at a point C on the circumference. ABC has maximum area. then find A & B in terms of the angle.
Can you try to find the area of the triangle in terms of the radius of the circle and the angle subtended? If you can do so, then its a simple problem in maximization.
For example, say the radius of the circle is r and the angle subtended at the point C is [tex]\theta[/tex] and the center of the circle is at the point [tex]O[/tex]. Also, the area of the triangle depends on the base and the height of the triangle, for the height to be maximum, the triangle MUST be isosceles for a given base, can you see why?
I feel in an isosceles triangle the base will be less but height will be more so how do we know that the area is maximum.