Area of an Inscribed Triangle in a Circle

Consider a circle with a radius of 10 cm. A triangle is inscribed within this circle, such that one of its vertices is at the center of the circle, and the other two vertices are on the circumference. If the angle at the center of the circle (the angle opposite the base of the triangle) is 60 degrees, what is the area of the triangle?

Recall that the area of a triangle can be calculated using the formula:

$$A = \f\frac{1}{2} \times \text{base} \times \text{height}$$