# Thread: help with this one problem

1. ## 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

2. Originally Posted by oohhoohh
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. $B(24, 0)$

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

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

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

5. $A(24, y_A)$

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

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