SOLUTION: A chord of length 16 sqrt3 is the perpendicular bisector of the radius in a circle. Determine the area of the circle.Please show me the steps

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Question 700877: A chord of length 16 sqrt3 is the perpendicular bisector of the radius in a circle. Determine the area of the circle.Please show me the steps
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A chord of length 16 sqrt3 is the perpendicular bisector of the radius in a circle.
Determine the area of the circle.Please show me the steps
:
We want to find the radius first.
A right triangle is formed by half the chord and half the radius and the radius
The radius is the hypotenuse, therefore using pythag; a^2 + b^2 = c^2
%288sqrt%283%29%29%5E2 + %28.5r%29%5E2 = r%5E2
64(3) + .25r^2 = r^2
192 = r^2 - .25r^2
192 = .75r^2
r^2 = 192/.75
r^2 = 156
r = sqrt%28256%29
r = 16
:
A = pi%2A16%5E2
A = 804.2477 sq units