In triangle ABC the bisector of angleB meets AC at D .A line PQ parallel to AC meets AB, BC and BD at P ,Q and R respectively. show that PR/RQ=BP/BQ

Asked by Harbans Singh | 10th Sep, 2015, 07:19: PM

Expert Answer:

I n space t h e space s m a l l space t r i a n g l e space B P Q comma space u sin g space a n g l e space b i s e c t o r space p r o p e r t y comma space w e space g e t fraction numerator B P over denominator B Q end fraction equals fraction numerator P R over denominator R Q end fraction... left parenthesis 1 right parenthesis F o r space t h e space a b o v e space t o space b e space t r u e comma space w e space d o space n o t space n e e d space P Q space t o space b e space p a r a l l e l space t o space A C. I f space t h e space q u e s t i o n space w a s space t o space s h o w space t h a t space fraction numerator P R over denominator R Q end fraction equals fraction numerator A D over denominator D C end fraction comma space t h e n space w e space w o u l d space p r o c e e d space a s space f o l l o w s colon I n space t h e space b i g g e r space t r i a n g l e space A B C comma space u sin g space a n g l e space b i s e c t o r space p r o p e r t y comma space w e space g e t fraction numerator A B over denominator B C end fraction equals fraction numerator A D over denominator D C end fraction... left parenthesis 2 right parenthesis A l s o comma space P Q vertical line vertical line A C. space S o space increment B P Q tilde increment B A C rightwards double arrow fraction numerator B P over denominator B A end fraction equals fraction numerator B Q over denominator B C end fraction rightwards double arrow fraction numerator B P over denominator B Q end fraction equals fraction numerator A B over denominator B C end fraction... left parenthesis 3 right parenthesis F r o m space left parenthesis 1 right parenthesis comma space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis comma space w e space g e t  fraction numerator P R over denominator R Q end fraction equals fraction numerator A D over denominator D C end fraction

Answered by satyajit samal | 11th Sep, 2015, 11:03: AM