An isosceles triangle $ABC$, with $AB = AC$, is inscribed in a fixed circle of radius 1 unit and

Question

An isosceles triangle $ABC$, with $AB = AC$, is inscribed in a fixed circle of radius 1 unit and centre $O$. It is given that angle $BOC = 2\theta$, where $\theta$ is acute. Using calculus, show that the area of the triangle $ABC$ is a maximum when it is equilateral. State the maximum value of this area exactly.[8]

Accepted Answer

The maximum area is $\dfrac{3\sqrt3}{4}$ square units, attained when $ABC$ is equilateral.

2024 NYJC P1 Q7

2024 NYJC P1 Q7

Video Solution:

Solution:

Solution locked