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

Question

In &#x394; ABC, &#x2220; B =35&#xB0;, &#x2220; C =65&#xB0; and the bisector of &#x2220; ABC meets BC in P . Arrange AP, BP and CP in descending order.

Philoid · Accepted Answer

Given: ∠B = 35°

∠C = 65°

The bisector of ∠ABC meets BC in P

We have to arrange AP, BO and CP in descending order

In Δ ACP, we have

∠ACP > ∠CAP

AP > CP (i)

In Δ ABP, we have

∠BAP > ∠ABP

BP > AP (ii)

From (i) and (ii), we have

BP > AP > CP

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