Question

D, E and F are the points on sides BC, CA and AB respectively of ∆ABC such that AD bisects ∠A, BE bisects ∠B and CF bisects ∠C. If AB = 5 cm, BC = 8 cm and CA = 4 cm, determine AF, CE and BD.

Answer 1

It is given that , and .

We have to find _, and BD.

Sinceis bisector of

So

Then,

$$\begin{gathered} \frac{5}{4}=\frac{BD}{BC-BD} \\ \Rightarrow \frac{5}{4}=\frac{BD}{8-BD} \\ \Rightarrow 40-5BD=4BD \\ \Rightarrow 9BD=40 \end{gathered}$$

So,

Since is the bisector of .

So,

$$\begin{gathered} \frac{AB}{BC}=\frac{AE}{EC} \\ \Rightarrow \frac{AB}{BC}=\frac{AC-EC}{EC} \end{gathered}$$

So

Now since is the bisector of

So

So

Hence

And