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

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(B) 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

$4$

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(B) 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: $\frac{AB}{AC} = \frac{BD}{DC}$.Substituting the given values: $\frac{8}{10} = \frac{3.2}{DC}$.Cross-multiplying gives: $8 	imes DC = 10 	imes 3.2$.$8 	imes DC = 32$.$DC = \frac{32}{8} = 4$.Therefore,the length of $DC$ is $4$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 8$,$AC = 10$ and $BD = 3.2$,then $DC = \ldots$

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