Question

The bisector of interior A of ∆ ABC meets BC in D. Bisector of exterior A meets BC produced in E. Prove that BD:BE = CD:CE.

Answer 1

Step-by-step explanation:

Given △ABC,AD bisects interior ∠A and AE bisects exterior ∠A meeting BC at D and BC produced at E.

To prove: BD/BE = CD/CE

Proof: In △ABC, AD bisects interior ∠A

∴ AB/AC = BD/DC (Angle bisector theorem) ..........1)

Similarly in △ABC, AE bisects exterior ∠A

∴ AB/AC BE/CE ...........2)

From equation (1) and (2)

AB/AC = BD/DC = BE/CE = CD/CE

Hence proved.