Triangle \(ACE\) is equilateral with side lengths of \(8.\) Points \(B\) and \(D\) are the midpoints of line segments

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by Vincen » Wed Nov 18, 2020 11:02 am

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Triangle \(ACE\) is equilateral with side lengths of \(8.\) Points \(B\) and \(D\) are the midpoints of line segments \(AC\) and \(CE\) respectively. Line segment \(BD\) is a diameter of the circle with center \(F.\) What is the area of the shaded region?

A. \(8\sqrt2 - 4\pi\)
B. \(12\sqrt3-2\pi\)
C. \(12\sqrt3 - 4\pi\)
D. \(16\sqrt3 - 2\pi\)
E. \(16\sqrt2 - 4\pi\)

Answer: B

Source: Princeton Review

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Triangle \(ACE\) is equilateral with side lengths of \(8.\) Points \(B\) and \(D\) are the midpoints of line segments

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Triangle \(ACE\) is equilateral with side lengths of \(8.\) Points \(B\) and \(D\) are the midpoints of line segments

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