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In the figure above, AC = BC = 8, angle C = 90°, and the circular arc : Problem Solving (PS)
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Re: In the figure above, AC = BC = 8, angle C = 90°, and the circular arc [#permalink]
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Area of shaded region = (area of circle/4) - area of triangle = (pi* 8^2)/4 - (8*8/4) = 16 pi - 32
Therefore answer is B

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Re: In the figure above, AC = BC = 8, angle C = 90°, and the circular arc [#permalink]
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Bunuel wrote:

In the figure above, AC = BC = 8, angle C = 90°, and the circular arc has its center at point C. Find the area of the shaded region.

A. \(8\pi-32\)
B. \(16\pi-32\)
C. \(16\pi-64\)
D. \(32\pi-32\)
E. \(32\pi-64\)


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

There’s not a single formula we can use to get the answer, but by combining a few formulas, we can calculate this.

First, think about the circle. The circle has radius r = 8, so its total area would be \(A=\pi{r^2}=64\pi\).
gm-tuaaof_img5

This entire figure is a quarter of the circle, so that area would be \(quarter \ circle=16\pi\).

Now, the shaded area (technically known as a circular segment), would have an area of
(circular segment) = (quarter circle) – (triangle ABC)

Well, we already have the area of the quarter circle. The triangle would have an area of (1/2)bh = 32. Therefore, the area of the segment is \(area=16\pi-32\).

Answer = (B)
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Re: In the figure above, AC = BC = 8, angle C = 90°, and the circular arc [#permalink]
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