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Math Help - square and angles problem

  1. #1
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    square and angles problem

    hey guys

    A---------E----F----B
    |..........................|
    |..........................|
    |..........................|
    |..........................|
    |..........................|
    C-------------------D
    ABCD is a aquare

    Prove angle ACE is half angle FCD

    thanks guys
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  2. #2
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    Quote Originally Posted by bloo.tomarto View Post
    hey guys

    A---------E----F----B
    |..........................|
    |..........................|
    |..........................|
    |..........................|
    |..........................|
    C-------------------D
    ABCD is a aquare

    Prove angle ACE is half angle FCD

    thanks guys
    Presumably E is meant to be halfway between A and B; and F is halfway between E and B?

    In that case, use some trigonometry to find the tan of each of those angles, and check that they are related by the formula \tan2\theta = \dfrac{2\tan\theta}{1-\tan^2\theta}. As an extra hint, draw a vertical line from F down to the side CD, in order to create a right-angled triangle containing the angle FCD.
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