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it is know that one vertex of triangle is located at point $A(2,-4)$ and equation of angle bisector of two another angle is given
1.$x+y-2=0$

2.$x-3*y-6=0$ we have to find equation of sides of triangle i have found point where this two line intersect ,got $(3,-1)$,not dont know how to get corrdinates of B and C vertices,i know that bisector cuts angle into two equal parts,also i know theorem of angle bisector,but how can i use it to find coordinates?

3 Answers 3

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If you reflect the point $A$ about the bisector of the angle at $B$ you get a point somewhere on $BC$. You get another point on $BC$ by reflecting about the other bisector. Now you know two points on $BC$...

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    it should be intersection of this two line yes?2012-06-19
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Yes find the third bissector is without utility. I replace this by explain mors the Henning Makholm solution: If we name $D_B$ and $D_C$ the bissectors and $A'=S_{D_B} (A)$ and $A''=S_{D_C}(A)$, then $A'$ and $A''$ are in line $(BC)$, so $B$ is the point intersection of $D_B$ and $(A'A'')$ and $C$ is the point intersection of $D_C$ and this $(A'A'')$. You need translate this using coordinates .

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    @Mohamed thanks for helping,you are welcome2012-06-19
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Find the image of A in both bisectors.These points will lie on the base.Now find the equation of the base from these two points.Now, solve the base with the given angle bisectors to get the points of other vertices and then finally find the equations of the remaining two sides.

Hope this helps.