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FIND THE COORDINATES OF THE CIRCUMCENTRE

OF A TRIANGLE WHOSE VERTICES ARE [8,6] , [8,-2]

And [2,-2] . ALSO FIND THE CIRCUMRADIUS

Asked by dalbirgolagarh | 18th Dec, 2015, 07:02: PM

Expert Answer:

$C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.$

$L e t space A open parentheses 8 comma 6 close parentheses comma space B open parentheses 8 comma negative 2 close parentheses space a n d space C open parentheses 2 comma negative 2 close parentheses space b e space t h e space v e r t i c e s space o f space t h e space t r i a n g l e space triangle A B C L e t space u s space f i n d space t h e space d i s tan c e s comma space A B comma space B C space a n d space C A A B equals square root of open parentheses 8 minus 8 close parentheses squared plus open parentheses 6 plus 2 close parentheses squared end root equals 8 space u n i t s B C equals square root of open parentheses 8 minus 2 close parentheses squared plus open parentheses negative 2 plus 2 close parentheses squared end root equals 6 space u n i t s C A equals square root of open parentheses 8 minus 2 close parentheses squared plus open parentheses 6 plus 2 close parentheses squared end root equals 10 space u n i t s rightwards double arrow 8 squared plus 6 squared equals 10 squared rightwards double arrow A B squared plus B C squared equals C A squared rightwards double arrow triangle A B C space i s space a space r i g h t space t r i a n g l e A space c i r c l e space w h i c h space p a s s e s space t h r o u g h space a l l space t h e space t h r e e space v e r t i c e s space o f space t h e space t r i a n g l e space i c a l l e d space t h e space c i r c u m c i r c l e. I n space t h e space a b o v e space f i g u r e comma space A C space s u b t e n d s space a space r i g h t space t i r a n g l e space a n d space h e n c e space A C space i s space t h e space d i a m e t e r space o f space t h e space c i r c l e. T h u s space t h e space c i r c u m r a d i u s space o f space t h e space c i r c l e equals fraction numerator A C over denominator 2 end fraction equals 10 over 2 equals 5 space u n i t s L e t space O open parentheses x comma y close parentheses space b e space t h e space c i r c u m c e n t r e space o f space t h e space c i r c u m c i r c l e. C i r c u m c e n t r e space i s space t h e space m i d p o i n t space o f space t h e space v e r t i c e s space A space a n d space C. T h u s space c o o r d i n a t e s space o f space t h e space c i r c u m c e n t r e space a r e colon x equals fraction numerator 8 plus 2 over denominator 2 end fraction comma space y equals fraction numerator 6 minus 2 over denominator 2 end fraction rightwards double arrow x equals 5 comma space y equals 2$

Answered by Vimala Ramamurthy | 19th Dec, 2015, 10:55: AM

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