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Math Help - Radius Of Circle

  1. #1
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    Radius Of Circle

    Let ABCD be a square with side lengths 10 of units. Let CDE be a equilateral triangle so that E is outside the square. What is the radius of a circle passing through points A,B and E
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  2. #2
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    Quote Originally Posted by X1337 View Post
    Let ABCD be a square with side lengths 10 of units. Let CDE be a equilateral triangle so that E is outside the square. What is the radius of a circle passing through points A,B and E
    Hi

    There may be a geometric solution but it can be solved by using coordinates (if you are allowed to).

    Let O be the midpoint of [AB].
    (OE) can be chosen as x-axis, and OB as y-axis.
    Spoiler:

    R = \frac{5(10-3\sqrt{3})}{4}
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by X1337 View Post
    Let ABCD be a square with side lengths 10 of units. Let CDE be a equilateral triangle so that E is outside the square. What is the radius of a circle passing through points A,B and E
    Draw a picture. Add the diameter that passes through E and the mid points of CD and AB. Call the mid point of AB F

    Now use the intersecting chord theorem to get AF.FB= (2r-EF)EF

    You should be able to claculate EF from what is given and AF=FB=5.

    CB
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