Geometry Question

• September 28th 2009, 02:26 AM
deltaxray
Geometry Question

THe diagram opposite shows an equilateral triangle ABC whose sides are 2(x) units long.

a) show that the inscribed circle tangent to all three sides has area 1/3pi(x)^2

b) show that the circumscribed circle passing through all three vertices has four times the area of the inscribed circle

Thanks

http://img39.imageshack.us/img39/2766/20681137.jpg
• September 28th 2009, 07:31 AM
red_dog
The radius of the inscribed circle is $r=\frac{l\sqrt{3}}{6}$, where $l$ is the length of the side of the triangle.

The radius of the circumscribed circla is $R=\frac{l\sqrt{3}}{3}$, where $l$ is the length of the side of the triangle.

Then use the formula for the area of a circle: $A=\pi R^2$