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Math Help - Geometry Question

  1. #1
    Junior Member
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    Geometry Question

    Can someone please help me with the following question please.

    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

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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    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
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