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# A circle inscribed in an equilateral triangle with side

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Senior Manager
Joined: 14 Jul 2006
Posts: 281
A circle inscribed in an equilateral triangle with side [#permalink]

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20 Aug 2006, 02:07
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A circle inscribed in an equilateral triangle with side length 10. What is the area of inscribed circle?
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Joined: 20 Nov 2005
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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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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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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Senior Manager
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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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Joined: 20 Nov 2005
Posts: 2894
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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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.
Attachments

Triangle.JPG [ 5.16 KiB | Viewed 809 times ]

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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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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
20 Aug 2006, 02:36
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