SOLUTION: A rectangle with dimension 5 by 8 is incribed in a circle. Wjat are the area and circumference of this circle? Also, find the area of the region inside the circle not covered by th

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Question 37892: A rectangle with dimension 5 by 8 is incribed in a circle. Wjat are the area and circumference of this circle? Also, find the area of the region inside the circle not covered by the rectangle. (Inscribed means inside with vertex's touching the edge of the circle.)
Answer by fractalier(6550) About Me  (Show Source):
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If you connect alternate vertices of an inscribed rectangle, it turns out to be a diameter of the circle. This is because a 90 degree inscribed angle cuts off 180 degrees of arc. This diameter's length can be found using the Pythagorean Theorem.
diam = sqrt(5^2 + 8^2) = sqrt(89)
radius = (1/2)sqrt(89)
A = pi(r^2)
A = (89/4)pi
C = 2(pi)r = pi(sqrt(89))
Area outside of rect = (89/4)pi - 40