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Sunday, May 3, 2009
Problem 22 - GMAT Geometry
An equilateral triangle of side 12 is inscribed in a circle, what is the area of the circle?
In an equilateral triangle, the height equals half the size times root 3. So here the height is 6 root 3. Since the triangle is inscribed in a circle, the radius is 2/3 of the height, so the radius is 4 root 3. The area will then be radius squared, or 48, times pi, choice C.
On this problem, how did you know the the radius is 2/3 of the height of an inscribed triangle? Is that the case for all inscribed triangles, or just equilateral triangles?
The three medians of the equilateral triangle intersect at a point 2/3 the way from a vertex, hence the radius r of such a circle is 2/3 the height of the equilateral triangle.
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In an equilateral triangle, the height equals half the size times root 3. So here the height is 6 root 3. Since the triangle is inscribed in a circle, the radius is 2/3 of the height, so the radius is 4 root 3. The area will then be radius squared, or 48, times pi, choice C.
ReplyDeleteAnswer C
ReplyDeleteOn this problem, how did you know the the radius is 2/3 of the height of an inscribed triangle? Is that the case for all inscribed triangles, or just equilateral triangles?
ReplyDeleteThe three medians of the equilateral triangle intersect at a point 2/3 the way from a vertex, hence the radius r of such a circle is 2/3 the height of the equilateral triangle.
ReplyDelete