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# Given an equilateral triangle ABC. What is the area of the

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Given an equilateral triangle ABC. What is the area of the [#permalink]

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16 Oct 2004, 06:13
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Given an equilateral triangle ABC. What is the area of the triangle?

(A) the radius of circle inscribed in ABC = 3

(B) the radius of circle circumscribed in ABC = 6
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17 Oct 2004, 08:56
I understand how B is correct. I don't see how A is correct plz explain
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17 Oct 2004, 12:20
Another for D

Not looking to solve the problem but info is suff to solve as there will always be one answer for a circle and equalateral triangle, inscribed or circumscribed.
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18 Oct 2004, 02:06
Maneesh wrote:
I understand how B is correct. I don't see how A is correct plz explain

Consider these truths:

1. Equilateral triangle meaning all angles 60degrees, correct ?
2. radious of inner circle + radious of circumcircle = perpendicular of equilateral triangle
3. perpendicular of an equilateral triangle = median of equilateral triangle = perpendicular bisector of equilateral triangle
4. thus, Circumcenter = orthocenter = incenter
5. and any side of an equilateral triangle = 2 * (perpendicular/ root 3)

cheers,
Dharmin
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18 Oct 2004, 08:39
Dharmin wrote:
Maneesh wrote:
I understand how B is correct. I don't see how A is correct plz explain

Consider these truths:

1. Equilateral triangle meaning all angles 60degrees, correct ?
2. radious of inner circle + radious of circumcircle = perpendicular of equilateral triangle
3. perpendicular of an equilateral triangle = median of equilateral triangle = perpendicular bisector of equilateral triangle
4. thus, Circumcenter = orthocenter = incenter
5. and any side of an equilateral triangle = 2 * (perpendicular/ root 3)

cheers,
Dharmin

and if that didn't clear it up, try this. The triangle must have 60 degrees all around, so a line drawn from the center of the circle will bisect that and make a 30 degree angle. So the triangle drawn in this diagram would have to be 30-60-90, which means you'd know everything. You could get the side of the triangle, or add the radius of the circle to the line drawn (3+6) and see that the height is 9.
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