Question

the internal bisector of angle abc meets BC at D and external bisector of angle A meets BC produced at e prove that BD upon BE is equal to CD upon CE​

Answer 1

Given — AD is angle bisector of ∠BAC and AE is angle bisector of exterior ∠.

To prove — BD/BE = CD/CE

Proof — Since AD ie interior ∠ bisector,

• AB/AC = BD/CD

Similarly, AE is exterior angle bisector,

• AB/AC = BE/CE

In both equations, AB/AC id comman therefore,

→ BD/CD = BE/CE

By cross multiplying we get,

→ BD/BE = CD/CE

Q.E.D