In Delta ABC, the bisector of angle A interse | vedclass

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(A) According to the Angle Bisector Theorem,if a ray bisects an angle of a triangle,then it divides the opposite side into segments that are proportio

Vedclass · Accepted Answer

$4.5$

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(A) According to the Angle Bisector Theorem,if a ray bisects an angle of a triangle,then it divides the opposite side into segments that are proportional to the other two sides of the triangle.In $\Delta ABC,$ since $AD$ is the bisector of $\angle A,$ we have the ratio:$\frac{AB}{AC} = \frac{BD}{DC}$Given values are $AB = 6,$ $BD = 4,$ and $DC = 3.$Substituting these values into the formula:$\frac{6}{AC} = \frac{4}{3}$Cross-multiplying to solve for $AC$:$4 	imes AC = 6 	imes 3$$4 	imes AC = 18$$AC = \frac{18}{4} = 4.5$Therefore,the length of $AC$ is $4.5$.

In $\Delta ABC,$ the bisector of $\angle A$ intersects $\overline{BC}$ at $D.$ If $AB = 6,$ $BD = 4$ and $DC = 3,$ find $AC$.

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