# ratio of circle to triangle

• Dec 14th 2010, 04:02 AM
rcs
ratio of circle to triangle
A triangle is formed inside a circle by connecting the center C to two
points A and B on the circle. If angle ACB = 30degrees, what is the ratio of the
areas of the circle to the triangle?

i want to find the area of the triangle but their is no measure of the sides so that i can find the area of the triangle. then area of a circle too
Call the radius $\displaystyle r$. The triangle will be isosceles and the two equal sides will be this length.
Area of circle: $\displaystyle \pi r^2$.
Area of triangle: $\displaystyle \frac{1}{2}\cdot r \cdot r \cdot \sin{30^{\circ}} = \frac{1}{2}\cdot r^2 \cdot \frac{1}{2} = \frac{1}{4}r^2$.
So the ratio of circle's area to triangle's area is $\displaystyle \frac{\pi r^2}{\frac{1}{4}r^2} = 4\pi$.
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