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# finding triangle circumcentre with equations for the triangle sides

Posted on 2010-01-12

Hi

I'm trying to find the triangle circumcentre from the equations for the triangle sides. I don't think I'm doing it right as I can't see how to finish the question off.

To get the circumcentre I need the point of intersection of 2 perpendicular bisectors. Given the equation of the side, the gradient of the bisector is -1/m but i don;t know how to get a point on this line to then work out the equation for the line using y - y1 = m(x - x1). I could say that the midpoint of the side is ((x1 + x2)/2, (y1 + y2)/2) and this point is on the perpendicular bisector but i don't know how to put this knowledge into y - y1 = m(x - x1). There's too many different x and y variables.

Once i have got the equation for one bisector i can get the others and then solve these equations simulataneously to get the midpoint.

The equations of the triangle are

y = 3x

y + 3x = 0

3y -x +12 = 0

Many thanks