Find the coordinates of circumcenter of a tri.ABC where A(1,2) , B(3,-4) , C(5,-6).
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Hi, 
Let the coordinates of the circumcentre of the triangle be (x, y).
Circumcentre of a triangle is equidistant from each of the vertices.

Distance between (1,2) and (x, y) = Distance between (3,-4) and (x, y)
x-12+y-22=x-32+y+42square x-12+y-22=x-32+y+42x2-2x+1+y2+4-4y= x2+9-6x+y2+16+8y 4x-12y-20 = 0 x-3y = 5 ....1also distance between 3,-4 and x,y= distance between 5,-6 and x,yx-32+y+42=x-52+y+62square x-32+y+42=x-52+y+62x2-6x+9+y2+16+8y= x2+25-10x+y2+36+12y 4x-4y=36 x-y = 9 ....2subtract equation 1 and 2 2y = 4 y = 2 so putting this in any equation x = 9+2 = 11

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