Asked by kusma1974 | 27th Jan, 2017, 02:25: AM

Expert Answer:

 
begin mathsize 16px style S i n c e space F space i s space t h e space m i d minus p o i n t space o f space B D comma space i n space t r i a n g l e space A B D comma
1 space. space stack A B with rightwards arrow on top space plus space 1 space. space stack A D with rightwards arrow on top space equals space left parenthesis 1 space plus space 1 right parenthesis space stack A F with rightwards arrow on top
rightwards double arrow stack A B with rightwards arrow on top space plus space stack A D with rightwards arrow on top space equals space 2 space stack A F with rightwards arrow on top space space space space space space space.... left parenthesis i right parenthesis
S i m i l a r l y comma space i n space t r i a n g l e space B C D comma
1 space. space stack C B with rightwards arrow on top space plus space 1 space. space stack C D with rightwards arrow on top space equals space left parenthesis 1 space plus space 1 right parenthesis space stack C F with rightwards arrow on top
rightwards double arrow stack C B with rightwards arrow on top space plus space stack C D with rightwards arrow on top space equals space 2 space stack C F with rightwards arrow on top space space space space space space space.... left parenthesis i i right parenthesis
A d d i n g space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis comma space w e space g e t
stack A B with rightwards arrow on top space plus space stack A D with rightwards arrow on top space plus space stack C B with rightwards arrow on top space plus space stack C D with rightwards arrow on top space equals space space 2 space stack A F with rightwards arrow on top space plus space space 2 space stack C F with rightwards arrow on top
rightwards double arrow stack A B with rightwards arrow on top space plus space stack A D with rightwards arrow on top space plus space stack C B with rightwards arrow on top space plus space stack C D with rightwards arrow on top space equals negative 2 space stack F A with rightwards arrow on top space minus space space 2 space stack F C with rightwards arrow on top
rightwards double arrow stack A B with rightwards arrow on top space plus space stack A D with rightwards arrow on top space plus space stack C B with rightwards arrow on top space plus space stack C D with rightwards arrow on top space equals negative 2 space left parenthesis stack F A with rightwards arrow on top space plus space space space stack F C with rightwards arrow on top right parenthesis
rightwards double arrow stack A B with rightwards arrow on top space plus space stack A D with rightwards arrow on top space plus space stack C B with rightwards arrow on top space plus space stack C D with rightwards arrow on top space equals negative 2 space left parenthesis 2 space stack F E with rightwards arrow on top right parenthesis
rightwards double arrow stack A B with rightwards arrow on top space plus space stack A D with rightwards arrow on top space plus space stack C B with rightwards arrow on top space plus space stack C D with rightwards arrow on top space equals 4 space stack E F with rightwards arrow on top

end style

Answered by Rashmi Khot | 27th Jan, 2017, 10:54: AM

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