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

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(C) 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

$6$

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(C) 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 $AB = 12$,$AC = 8$,and $BD = 9$,we substitute these values into the equation:$\frac{12}{8} = \frac{9}{DC}$Simplifying the fraction $\frac{12}{8}$ gives $\frac{3}{2}$.So,$\frac{3}{2} = \frac{9}{DC}$Cross-multiplying,we get $3 	imes DC = 9 	imes 2$$3 	imes DC = 18$$DC = \frac{18}{3} = 6$Therefore,the length of $DC$ is $6$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 12$,$AC = 8$ and $BD = 9$,find $DC$.

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