Question

The bisector of the exterior angle ∠A of Δ ABC intersects side BC produced at D. Prove that
AB / AC = BD / DC.

Answer 1

Given: ABC is a triangle; AD is the exterior bisector of 4A and meets BC
produced at D; BA is produced to F.
To prove: AB/AC = BD/DC
Construction: Draw CE||DA to meet AB at E.
Proof: In A ABC. CE||AD cut by AC.

∠CAD = ∠ACE (Alternate angles)
Similarly CE || AD cut by AB

∠FAD = ∠AEC (corresponding angles)
AC = AE (by isosceles △ theorem)

Now in △BAD, CE || DA 
AE = DC (BPT)
AB BD

But AC = AE (proved above)
AC = DC 
AB = BD or
AB/AC = BD/DC (proved).   

Answer 2

Answer:

Step-by-step explanation: