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# how to find the centroid, circumcenter and orthocenter of a triangle?

Sat 2 Jan, 2010 05:13 pm
i need some help on this problem
i have to find the centroid, circumcenter and orthocenter of a triangle. this points are
X (73,33)
Y(33,35)
Z(52,27)

Can someone write it out algebraicly? thanks in advance.
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uvosky

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Mon 28 May, 2012 01:52 am
@fuyu1993,
If ( m , n ) ; ( u , v ) and ( p , q ) are the vertices of a triangle then
( (m+u+p) /3 , (n+v+q) /3 ) is the centroid ; if ( k , s ) is the circumcenter
then k and s can be found by solving ,
(n - v) / ( u - m ) = ( 2k - m - u ) / ( 2s - v - n ) ..... ( i )
( v - q ) / ( p - u ) = ( 2k - p - u ) / ( 2s - v - q ) ..... ( ii )
if ( w , f ) is the orthocenter then w and f can be found by solving ,
( f - n ) / ( w - m ) = ( u - p ) / ( q - v ) ..... ( 1 )
( f - v ) / ( w - u ) = ( m - p ) / ( q - n ) ..... ( 2 )
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