Bisectors of angle B and Cof a triangle intersect each other at point 'O'.Prove thatangle BOC=
90ring operator +1/2angleA

Asked by Delin | 31st Aug, 2014, 02:46: PM

Expert Answer:

Consider the following triangle.
I n space t r i a n g l e space A B C comma space b y space a n g l e space s u m space p r o p e r t y comma space w e space h a v e comma angle A plus angle B plus angle C equals 180 degree rightwards double arrow fraction numerator angle A plus angle B plus angle C over denominator 2 end fraction equals fraction numerator 180 degree over denominator 2 end fraction space space space space space space open square brackets d i v i d i n g space b y space 2 space f r o m space b o t h space t h e space s i d e s close square brackets rightwards double arrow fraction numerator angle A over denominator 2 end fraction plus fraction numerator angle B over denominator 2 end fraction plus fraction numerator angle C over denominator 2 end fraction equals 90 degree rightwards double arrow fraction numerator angle B over denominator 2 end fraction plus fraction numerator angle C over denominator 2 end fraction equals 90 degree minus fraction numerator angle A over denominator 2 end fraction.... left parenthesis 1 right parenthesis N o w space c o n s i d e r space t h e space t r i a n g l e space triangle B O C A g a i n space b y space a n g l e space s u m space p r o p e r t y comma space w e space h a v e comma fraction numerator angle B over denominator 2 end fraction plus fraction numerator angle C over denominator 2 end fraction plus angle B O C equals 180 degree rightwards double arrow angle B O C equals 180 degree minus open parentheses fraction numerator angle B over denominator 2 end fraction plus fraction numerator angle C over denominator 2 end fraction close parentheses rightwards double arrow angle B O C equals 180 degree minus open parentheses 90 degree minus fraction numerator angle A over denominator 2 end fraction close parentheses rightwards double arrow angle B O C equals 180 degree minus 90 degree plus fraction numerator angle A over denominator 2 end fraction rightwards double arrow angle B O C equals 90 degree plus fraction numerator angle A over denominator 2 end fraction

Answered by Vimala Ramamurthy | 1st Sep, 2014, 09:31: AM