posted by Zach .
Help I need help to find the coordinates of the circumcenter of each triangle. Isosceles triangle CDE with vertices C(0, 6), D(0, –6), and E(12, 0)
the circumcenter is the intersection of the perpendicular bisectors of the sides.
The midpoint of CD = (0,0)
The slope of CD is -12/0 is undefined, so CD is vertical
The perpendicular bisector is horizontal.
You want the line through (0,0) with slope 0 is the line y=0.
The midpoint of DE = (6,-6)
The slope of DE is 6/12 = 1/2
You slope of the bisector is -2
The line through (6,-6) with slope -2 is
y+6 = -2(x-6), or y = -2x + 6
the two bisectors intersect at (0,3), which is the circumcenter.
as usual, check my math.