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Math Help - Trapezoid Inscribed in a circle

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    Trapezoid Inscribed in a circle

    A circle wih R=24 has a inscribed trapezoid with the largest base twice as long as other base and the two sides.
    Question: How do I find the length of the sides of the trapezoid and its area?

    I'm thinking the only way for this to be possible is for the largest base to be the length of diameter of circle? I'm a bit lost.
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    Senior Member abhishekkgp's Avatar
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    Re: Trapezoid Inscribed in a circle

    Quote Originally Posted by Aquameatwad View Post
    A circle wih R=24 has a inscribed trapezoid with the largest base twice as long as other base and the two sides.
    Question: How do I find the length of the sides of the trapezoid and its area?

    I'm thinking the only way for this to be possible is for the largest base to be the length of diameter of circle? I'm a bit lost.
    your answer satisfies the given conditions.. so it correct.. show that its the only answer.
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    Re: Trapezoid Inscribed in a circle

    It does seem a bit tricky.

    But I agree that the largest base to be the length of diameter of circle. Therefore the parallel sides will be 24 and 48. Then you need to apply pythagoras thm to find the diagnol sides.
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    Re: Trapezoid Inscribed in a circle

    Quote Originally Posted by pickslides View Post
    It does seem a bit tricky.

    But I agree that the largest base to be the length of diameter of circle.Therefore the parallel sides will be 24 and 48. Then you need to apply pythagoras thm to find the diagnol sides.
    Why?
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    Re: Trapezoid Inscribed in a circle

    Yikes. So is there some property of circumscribed circles or trapezoids that proves this to be true? i assumed the largest base was the diameter but im not really sure why...
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    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Trapezoid Inscribed in a circle

    Quote Originally Posted by Aquameatwad View Post
    Yikes. So is there some property of circumscribed circles or trapezoids that proves this to be true? i assumed the largest base was the diameter but im not really sure why...

    Solution:

    An isosceles trapezoid is inscribed in a circle - Math Central
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    Re: Trapezoid Inscribed in a circle

    Hello, Aquameatwad!

    I don't believe the problem is asking for the largest possible base.


    A circle wih R=24 has a inscribed trapezoid with the largest ? base
    twice as long as other base and the two sides.
    Find the length of the sides of the trapezoid and its area?

    I think it is referring to the longer base:
    . . "The longer base is twice as long as the other base and the two sides."

    Then the trapezoid looks like this:

    Code:
                     24
                * - - - - - *
               / .         . \
              /   .       .   \
          24 /     .     .     \ 24
            /       .   .       \
           /         . .         \
          * - - - - - * - - - - - *
               24          24

    The trapezoid is half of a regular hexagon.
    It is comprised of three equilateral triangles with side 24.

    You should be able to calculate its area.

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