Find the co-ordinates of the circumcentre of the triangle whose vertices have co-ordinates (-4,5) (2,1) and (2,4)

Asked by Sambandan | 5th Mar, 2015, 01:21: PM

Expert Answer:

L e t 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 t r i a n g l e space b e space O left parenthesis x comma y right parenthesis comma space A left parenthesis negative 4 comma 5 right parenthesis comma space B left parenthesis 2 comma 1 right parenthesis space a n d space C left parenthesis 2 comma 4 right parenthesis D i s tan c e space f r o m space t h e space c i r c u m c e n t r e space t o space t h e space v e r t i c e s space s h o u l d space b e space e q u a l space a s space t h e y space r e p r e s e n t space t h e space c i r c u m r a d i u s O A equals O B square root of left parenthesis x plus 4 right parenthesis squared plus left parenthesis y minus 5 right parenthesis squared end root equals square root of left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared end root rightwards double arrow left parenthesis x plus 4 right parenthesis squared plus left parenthesis y minus 5 right parenthesis squared equals left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared rightwards double arrow x squared plus 8 x plus 16 plus y squared minus 10 y plus 25 equals x squared minus 4 x plus 4 plus y squared minus 2 y plus 1 rightwards double arrow 12 x minus 8 y equals negative 36 rightwards double arrow 3 x minus 2 y equals negative 9........... left parenthesis i right parenthesis O A equals O C square root of left parenthesis x plus 4 right parenthesis squared plus left parenthesis y minus 5 right parenthesis squared end root equals square root of left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 4 right parenthesis squared end root rightwards double arrow left parenthesis x plus 4 right parenthesis squared plus left parenthesis y minus 5 right parenthesis squared equals left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 4 right parenthesis squared rightwards double arrow x squared plus 8 x plus 16 plus y squared minus 10 y plus 25 equals x squared minus 4 x plus 4 plus y squared minus 8 y plus 16 rightwards double arrow 12 x minus 2 y equals negative 21........... left parenthesis i i right parenthesis  S o l v 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 x equals negative 4 over 3 comma space y equals 5 over 2 T h e space c i r c u m c e n t r e space o f space t h e space t r i a n g l e space i s space open parentheses negative 4 over 3 comma 5 over 2 close parentheses.

Answered by Prasenjit Paul | 6th Mar, 2015, 12:08: PM

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