Question

Find the area of the largest isosceles triangle inscribed in a semicircle of radius 10ft., the vertex of the triangle being at the center of the circle.

Answer 1

The area of isosceles triangle can be found by the following expression:
S = 1/2 a2 sin θ
The largest value of S would be then sin θ = 1, thus θ = 90 degree.
Thus
S = 1/2 10² = 50 ft².