Find the equation of circumcircle of the triangle whose sides are `2x +y = 4,x + y = 6 and x +2y=5`.

Explanation

First we will find the co-ordinates of the vertices of a triangle
`:.` On solving two-two equations, we get the vertices as `(-2,8),(7,-1) and (1,2)`
Let the equation of circle be
`x^(2)+y^(2)+2gx+2fy+c=0`....(1)
This circle passes through the point `(-2,8)`
`4+64 -4g +16f + c=0`
`rArr -4g +16f +c = -68` .....(2)
This circle passes through the point `(7,-1)`
`49 +1 +14g-2f +c=0`
`rArr 14g - 2f +c = -50` ....(3)
This circle passes through the point (1, 2)
`1+4+2g+4f +c=0`
`rArr2g+4f+c=-5`....(4)
From eqs. (2),(3) and (4)
`g=-(17)/(2),f=-(19)/(2),c=50`
From eq. (1), equation of circle
`x^(2)+y^(2)-17x-19y+50=0`.