Question

bisector of exterior angle CAF of triangle ABC, intersects side BC produced at D. Show that BA/AC = BD/DC

Answer 1

Answer:

The proved is explained below.

Step-by-step explanation:

Given bisector of exterior angle CAF of triangle ABC, intersects side BC produced at D. we have to prove that $\frac{BA}{AC}=\frac{BD}{DC}$

Construct BE||AD

∠1=∠2 and ∠3=∠4 due to corresponding and alternate angles. Also ∠1=∠3 given

⇒∠2=∠3

∴ΔBAE is isosceles gives AE=EB

From side-splitting theorem

$\frac{AE}{AC}=\frac{BD}{DC}$

⇒  $\frac{BA}{AC}=\frac{BD}{DC}$

Hence proved