Question

let $ab = 8$, $bd = 4$, and $ac = 10$. calculate $dc$. image not set to scale.
options:
6.34
5
3.07
none of these answers are correct.
5.63

Explanation:

Step1: Apply Angle Bisector Theorem

The Angle Bisector Theorem states that if a bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. So, $\frac{BD}{DC}=\frac{AB}{AC}$.

Step2: Substitute known values

We know $AB = 8$, $BD = 4$, and $AC = 10$. Substitute these into the formula: $\frac{4}{DC}=\frac{8}{10}$.

Step3: Solve for DC

Cross - multiply: $8\times DC=4\times10$. Then $8DC = 40$. Divide both sides by 8: $DC=\frac{40}{8}=5$.

Answer:

5