What is the area of the circle?
Consider the following for the next three (03) items that follow:<br>In the figure given below, a circle is inscribed in a square PQRS. A rectangle at the corner P that measures 4\text{ cm} \times 2\text{ cm} and a square at the corner R are drawn.
- A. 100\pi square cm ✓
- B. 96\pi square cm
- C. 50\pi square cm
- D. 48\pi square cm
Correct Answer: A. 100\pi square cm
Explanation
Let the radius be R. The circle touches the rectangle's inner vertex, giving the distance relation (R-4)^2 + (R-2)^2 = R^2 \implies R^2 - 12R + 20 = 0. Since R \gt 4, R=10. The circle's area is \pi R^2 = 100\pi.
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