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Math Help - ratio of circle to triangle

  1. #1
    rcs
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    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
    please help me on this problem...
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    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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    Prove it ... thank u so so much... Your are one of the Bests in MHF
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