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Thread: help with this one problem

  1. #1
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    help with this one problem

    CD bisects angle ACB. Point D has coordinates (24,10). Find the coordinates of point A.

    diagram 123 :: untitled.jpg picture by ooorandomooo - Photobucket
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  2. #2
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    Quote Originally Posted by oohhoohh View Post
    CD bisects angle ACB. Point D has coordinates (24,10). Find the coordinates of point A.

    diagram 123 :: untitled.jpg picture by ooorandomooo - Photobucket
    1. $\displaystyle B(24, 0)$

    2. $\displaystyle \tan(\angle( BCD))=\frac{10}{24}=\frac5{12}$

    3. $\displaystyle \angle(BCA) = 2 \cdot \angle( BCD)$

    4. $\displaystyle \tan(2\alpha)=\dfrac{2 \tan(\alpha)}{1-(\tan(\alpha))^2}$

    5. $\displaystyle A(24, y_A)$

    $\displaystyle y_A = 24 \cdot \tan(\angle(BCA))$


    6. I've got $\displaystyle A\left(24\ ,\ \frac{2880}{119}\right)$
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