Question

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Answer 1

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Answer 2

Question;-

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

Method of Solution;-

Given: ABC is a triangle in which AD is the exterior bisector of A and meets BC

produced at D and  BA is produced to F.

To prove: AB/AC = BD/DC

Construction: Draw CE||DA to meet AB at E.

Proof: In A    ∆ABC in which CE||AD cut by AC.

∠CAD = ∠ACE  -'- (Alternate angles)

Now,

Similarly CE || AD cut in

line  AB

∠FAD = ∠AEC -'- (corresponding angles)

Again,

AC = AE (by using isosceles △ theorem)

Considering in △BAD whereCE || DA 

AE = DC -'- (BPT)

Similarly,

AC = DC 

Now,

AB/AC = BD/DC

proved!!!  

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