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ans is A,B
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Asked by jatinmankar | 18 May, 2019, 00:18: AM
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A left parenthesis 3 comma 1 right parenthesis space a n d space m i d p o i n t space o f space B C space i s space M open parentheses 5 over 2 comma 7 over 2 close parentheses S i n c e comma space M space i s space t h e space m i d p o i n t space o f space B C space a n d space c o o r d i n a t e s space o f space B space a n d space C thin space a r e space left parenthesis x subscript 1 comma y subscript 1 right parenthesis space a n d space left parenthesis x subscript 2 comma y subscript 2 right parenthesis space r e s p rightwards double arrow open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction comma fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction close parentheses equals open parentheses 5 over 2 comma 7 over 2 close parentheses rightwards double arrow x subscript 1 plus x subscript 2 equals 5 space a n d space y subscript 1 plus y subscript 2 equals 7 rightwards double arrow vertical line x subscript 1 plus x subscript 2 vertical line plus vertical line y subscript 1 plus y subscript 2 vertical line equals 12 T h u s comma space o p t i o n space i s space c o r r e c t N o w comma space w e space k n o w space t h a t space t h e space c e n t r o i d space G left parenthesis x comma y right parenthesis space o f space a space t r i a n g l e space d i v i d e s space t h e space m e d i a n space i n space t h e space r a t i o space 2 colon 1 space a n d space A M thin space i s space t h e space m e d i a n rightwards double arrow open parentheses x comma y close parentheses equals open parentheses fraction numerator 1 cross times 3 plus 2 cross times begin display style 5 over 2 end style over denominator 1 plus 2 end fraction comma fraction numerator 1 cross times 1 plus 2 cross times begin display style 7 over 2 end style over denominator 1 plus 2 end fraction close parentheses equals open parentheses 8 over 3 comma 8 over 3 close parentheses rightwards double arrow C e n t r o i d space i s space G open parentheses 8 over 3 comma 8 over 3 close parentheses L e t space O open parentheses a comma b close parentheses space b e space t h e space c i r c u m space c e n t r e space o f space t r i a n g l e space A B C W e space k n o w space t h a t space t h e space c e n t r o i d space G space d i v i d e s space O H space i n space t h e space r a t i o space 1 colon 2 U sin g space s e c t i o n space f o r m u l a comma space w e space h a v e open parentheses fraction numerator 2 cross times a plus 1 cross times 0 over denominator 2 plus 1 end fraction comma fraction numerator 2 cross times b plus 1 cross times 2 over denominator 2 plus 1 end fraction close parentheses space equals open parentheses 8 over 3 comma 8 over 3 close parentheses rightwards double arrow fraction numerator 2 a over denominator 3 end fraction equals 8 over 3 space a n d space fraction numerator 2 b plus 2 over denominator 3 end fraction equals 8 over 3 rightwards double arrow a equals 4 space a n d space b equals 3 rightwards double arrow vertical line a minus b vertical line equals 1 S o comma space o p t i o n space C thin space i s space n o t space c o r r e c t H O equals square root of open parentheses 0 minus 4 close parentheses squared plus left parenthesis 2 minus 3 right parenthesis squared end root equals square root of 17 rightwards double arrow H O squared equals 17 T h e r e f o r e comma space D space i s space a l s o space i n c o r r e c t H e n c e comma space o p t i o n space B space i s space o n l y space c o r r e c t.
Answered by Renu Varma | 18 May, 2019, 10:45: AM

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