Question

find the circumcentre of the triangle firmed by the lines. x+y=0,2x+y+5=0, x-y=2

Answer 1

first find point of intersection of all line
e.g vertices of triangle
is (-5,5) (1,-1) and (-1,-3)
now
find find midpoint of (-5,5) and (-1,-3)
e.g. (-3,1)
now equation of line which passes through (-3,1) and perpendicular to 2x+y+5=0 is
(y-1)=1/2(x+3)

x-2y+5=0 ------(1)
again midpoint of (1,-1) and (-1,-3) is (0,-2)
now equation of line which passes through (0,-2) and perpendicular to x-y=2
is
x+y+2=0 --------(2)
solve equation (1) and (2)
x=-3 and y=1
hence circumcentre is (-3,1)