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In the diagram below, line segment $AT$ is a diameter of the circle with center $O$. What is the area of the shaded part of the circle?

enter image description here

$AT= 16$.

Half of the circles area is equal to $100.48$, on the other half of the circle there is a triangle spitting it up, The triangle is a right triangle with interior angle measures of $30, 60$, and $90$. There is one side known and that side is the diameter which is equal to $16$, it is the hypotenuse of the triangle.

Amzoti
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Matthew
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    What diagram? You likely cannot post graphics here yet. – Ron Gordon May 29 '13 at 21:14
  • Nope can't post pictures. But you can see it here: http://assets.openstudy.com/updates/attachments/51a620f6e4b041f5501d42f5-matthewjames-1369841949051-circcccc.png – Matthew May 29 '13 at 21:23

1 Answers1

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Sides of a 30-60-90 triangle of hypotenuse $16$ are $8$ and $8 \sqrt{3}$. The area of that triangle is then $(1/2) (8)(8 \sqrt{3}) = 32 \sqrt{3}$. The shaded area is then the area of the circle minus the area of that triangle, or $64 \pi - 32 \sqrt{3}$.

Ron Gordon
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