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GRE
GRE Quantitative Reasoning Section

Comparing Areas in an Inscribed Triangle and Circular Segment

Very Hard Geometry Circles

Consider a circle with a radius of $r$. Inside this circle, a triangle is inscribed such that one of its vertices is located at the center of the circle, while the other two vertices lie on the circumference. The angle formed at the center of the circle by the lines drawn to these two vertices is denoted as $\theta$ (in radians). The lengths of the sides of the triangle can be expressed in terms of the radius $r$ and the angle $\theta$.

Let Quantity A be the area of the inscribed triangle, and let Quantity B be the area of the circular segment (the area of the circle minus the area of the triangle) opposite the angle $\theta$. What can you conclude about the relationship between Quantity A and Quantity B?

Hint

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