In `triangle ABC` internal angle bisector AI,BI and CI are produced to meet opposite sides in `A',B',C'` respectively. Prove that the maximum value of `(AIxxBIxxCI)/(A A'xxBB'xxCC')` is `8/27`

In /_ABC internal angle bisector AI,BI and CI are produced to meet opposite sides in A',B',C' respectively.Prove that the maximum value of (AI xx BI xx CI)/(AA'xx BB'xx C') is (8)/(27)

The bisectors of the angles B and C of a triangle ABC, meet the opposite sides in D and E respectively.If DE|BC, prove that the triangle is isosceles.

In a triangle ABC, the bisector of angle A meets the opposite side at D.Using vectors prove that BD:DC=c:b.

In Delta ABC with fixed length of BC, the internal bisector of angle C meets the side AB at D and meet the circumcircle at E. The maximum value of CD xx DE is

In a triangle ABC , the sides a , b , c are in G.P., then the maximum value of angleB is

In triangle ABC, if A = 2B, and the sides opposite to the angles A, B, C are alpha+1,alpha-1andalpha respectively, then alpha =

In a triangle ABC , angle A=72^@ . Its sides AB and AC are produced to the points D and E respectively. If the bisectors of the angle CBD and angle BCE meet at point O, then angle BOC is equal to: