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GRE
GRE Quantitative Reasoning Section

Comparison of Areas in a Circle

Hard Geometry Circles

In a circle with center O, a radius of length $r$, and a sector that subtends an angle of $ heta$ radians at the center, we will analyze two quantities:

Quantity A: The area of the sector of the circle.

Quantity B: The area of the isosceles triangle formed by the two radii and the chord that connects their endpoints.

Given that the angle $ heta$ is $\frac{\frac{ icef\frac{ ext{π}}{2}}{ ext{r}}}{2}$ and the radius $r = 10$, determine the relationship between Quantity A and Quantity B.

Hint

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