Question

In Δ ABC, ∠B = 35°, ∠C = 65° and the bisector of ∠BAC meets BC in P. Arrange AP, BP and CP in descending order.

Answer 1

It is given that

∠B = 35°

∠C = 65°

AP is the bisector of ∠CAB

We have to arrangeAP, BPand CPin descending order.

In  ΔACP we have

∠ACP = 65°

∠CAP = 40°(As AP is the bisector of ∠CAB

So  AP > CP (Sides in front or greater angle will be greater)              ........(1)

In  ΔABP we have

∠BAP = 40°(As AP is the bisector of ∠CAB)

Since, 

∠BAP >∠ABP

So  BP > AP                ..........(2)

Hence 

From (1) & (2) we have

 BP > AP > CP