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A circle inscribed in an equilateral triangle with side

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apollo168
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A circle inscribed in an equilateral triangle with side [#permalink] New post   20 Aug 2006, 02:07
A circle inscribed in an equilateral triangle with side length 10. What is the area of inscribed circle?



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Re: A circle inscribed in an equilateral triangle with side [#permalink] New post   20 Aug 2006, 02:18
25PI/3

When the perpendiculars are dropped from the vertices of the triangles then they meet at the centroid of the circle and the centroid will co-incide with the center of the circle. The ratio of length of line from vertex to centroid to line from centroid to side is 2:1.

So length of perpendicular = √(100-25) = 5*√3
Radius of circle = (5*√3)/3 = 5/√3
Area = 25PI/3
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Re: A circle inscribed in an equilateral triangle with side [#permalink] New post   20 Aug 2006, 02:22
Hi PS_dahiya

Your answer to this one coincides with the question bank's. What do you mean when you say centroid?
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Re: A circle inscribed in an equilateral triangle with side [#permalink] New post   20 Aug 2006, 02:31
apollo168 wrote:
Hi PS_dahiya

Your answer to this one coincides with the question bank's. What do you mean when you say centroid?

In the figure attached. meeting point of the three perpendiculars is the centroid.
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Triangle.JPG
Triangle.JPG [ 5.16 KiB | Viewed 1446 times ]

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Re: A circle inscribed in an equilateral triangle with side [#permalink] New post   20 Aug 2006, 02:36
Oh I get it. So the lower two triangles created are two 30-60-90 triangles so from there you can solve for the radius. Thanks for the diagram :)



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Re: A circle inscribed in an equilateral triangle with side [#permalink]
20 Aug 2006, 02:36
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