Q5 of 76 Page 11

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


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


More from this chapter

All 76 →
3

In Δ ABC, side AB is produced to D so that BD=BC. If ∠B=60° and ∠A=70°, prove that:

(i) AD > CD (ii) AD > AC

 4

Is it possible to draw a triangle with sides of length 2 cm, 3 cm, and 7 cm?

 6

O is any point in the interior of Δ ABC. Prove that

(i) AB + AC > OB + OC


(ii) AB + BC + CA > OA + OB + OC


(iii) OA + OB + OC > (AB + BC + CA)

 7

Prove that the perimeter of a triangle is greater than the sum of its altitudes.