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

$2.1$

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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 values are $AB = 5$,$AC = 4.2$,and $BD = 2.5$.Substituting these values into the equation:$\frac{5}{4.2} = \frac{2.5}{DC}$$5 	imes DC = 4.2 	imes 2.5$$5 	imes DC = 10.5$$DC = \frac{10.5}{5}$$DC = 2.1$Thus,the length of $DC$ is $2.1$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $BD = 2.5$,$AB = 5$ and $AC = 4.2$,find $DC$.

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