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

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(C) According to the Angle Bisector Theorem,the bisector of an angle of a triangle divides the opposite side into segments that are proportional to th

Vedclass · Accepted Answer

$16$

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(C) According to the Angle Bisector Theorem,the bisector of an angle of a triangle 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 $BC = 21$ and $BD = 9$,we can find $DC$ as: $DC = BC - BD = 21 - 9 = 12$.Substituting the known values into the theorem: $\frac{12}{AC} = \frac{9}{12}$.Cross-multiplying gives: $9 	imes AC = 12 	imes 12$.$9 	imes AC = 144$.$AC = \frac{144}{9} = 16$.Therefore,the length of $AC$ is $16$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 12$,$BD = 9$ and $BC = 21$,find $AC$.

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