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31 Dec 2005, 23:18
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A circle inscribed in an equilateral triangle with side length 20. What is the area of inscribed circle?
No OA available. Just try!
No OA available. Just try!
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31 Dec 2005, 23:27
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vivek123
draw a triangle by adding the mid point of each side of the equilateral triangle. this new trangle, also equilateral trangle, is inscribed in the circle. the side of the new equi trangle is 10.
so r = a/sqrt 3 = 10/sqrt(3)
Area of the circle = pi (10/sqrt(3))^2 = (100/3) (pi)
01 Jan 2006, 17:45
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another way to solve this could be...
draw perpendicular bisectors of each angle. They should meet at the centroid of the triangle which is the center of the circle. the radius of the circle is 1/3 the length of the bisector.
or
length of bisector x = [(20)^2-(10)^2]^1/2 = 300^1/2
area = pi*300*1/3*1/3 = 100pi/3
draw perpendicular bisectors of each angle. They should meet at the centroid of the triangle which is the center of the circle. the radius of the circle is 1/3 the length of the bisector.
or
length of bisector x = [(20)^2-(10)^2]^1/2 = 300^1/2
area = pi*300*1/3*1/3 = 100pi/3
