Posted by Anonymous on .
Triangle with vertices:
D(18,12)
E(6,12)
F(12,6)
Show that the right bisectors of the sides of triangleDEF all intersect at point C(4,4), the circumcentre of the triangle.
I found the midpoint of DF then the slope of the midpoint and point E, then found y intercept of new point (midpoint I labelled A) I then subbed point C into the equation of the line found. But it doesn't seem to be equally each other as they should...help!

Math 
Reiny,
Problem #1 is that you are not finding the rightbisector, but rather the medians
I will describe the steps to find your first rightbisector
1. the midpoint of DF is A(3, 9)
2. slope of DF = 6/30 =  1/5
3. So the slope of the rightbisector of DF is +5
4. equation of rightbisector is
y = 5x + b , but A(3,9) lies on it, so
9 = 5(3) + b
b = 24
rightbisector of DF is y = 5x + 24
repeat those steps for one of the other sides
solve those two equations, you should get (4,4)
Find the equation of the third side, using the above steps
Sub in (4,4) to see if it satisfies the third equation, it should !! 
Math 
Anonymous,
Thanks!!