Question

In triangle ABC AB is lesser than AC PB is bisector of angle B PC is bisector of angle C prove that PBis lesser than PC

Answer 1

The solution is attached as a word file

1b7a89fccb30df4aa166dc906629b9ca.doc

Answer 2

In the triangle ABC, AB is lesser than AC

Since angle C is opposite to AB and B is opposite to AC.

AB is lesser than AC

Angle C is lesser than angle B

Since the angle opposite to shorter side is smaller and vice versa.

½ of angle C will be less than ½ of angle B

The inverse of the above theorem will be, the line opposite to the smaller angle is small and vice versa

Since P bisect B and C hence,

PB is lesser than PC