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

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Question

(A) 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

$BD = 2.5, DC = 3.5$

Vedclass · Answer

(A) 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.Therefore,$\frac{BD}{DC} = \frac{AB}{AC}$.Given $AB = 10$ and $AC = 14$,we have $\frac{BD}{DC} = \frac{10}{14} = \frac{5}{7}$.Let $BD = 5x$ and $DC = 7x$.Since $BC = BD + DC = 6$,we have $5x + 7x = 6$,which implies $12x = 6$,so $x = 0.5$.Thus,$BD = 5(0.5) = 2.5$ and $DC = 7(0.5) = 3.5$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 10$,$BC = 6$,and $AC = 14$,find $BD$ and $DC$.

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