Question

The circumventer of a triangle firmed by the lines y=x , y=2x , y=3x+4 is?

Coordinates of circumcentre?

Answer 1

Since circumcentre P(x,y) is equidistance from the vertices of the triangle A(0,0) , B(-2,-2) , C(-4,-8) we have AP=CP and AP=BP
Or x²+y²= (x+4)² + (y+8)²

8x+16y+80 = 0 _eq1

And x²+y² = (x+2)² + (y+2)²
Or 4x+4y+8=0 _eq2 Solving eq1 and eq2 we get y= -8 and x=6