The bisector of interior A of ∆ ABC meets BC in D. Bisector of exter

1.	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» 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.

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»

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.

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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.

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