Question

Help Please? Will Give Medal!


Find the circumcenter of ΔEFG with E(3, 6), F(3, 4), and G(7, 4).
A. (5, 5)
B. (3, 6)
C. (4, 6)
D. (6, 4)

Answer 1

The center is the intersection of the perpendicular bisectors of the sides.
you only need two of the perpendicular bisectors to find their intersection.
To see this, just imagine the side of the triangle as a chord of the circle. The center of the circle needs to be on the perpendicular bisector of the chord.
To get the perpendicular bisector (I mean the equation of the line for this), first find the midpoint of the side of the triangle (you have the two endpoints and you know the midpoint formula, right?). Now you have a point on the line, you just need the slope. But the slope is the negative reciprocal of the the slope of the side of the triangle, as they are perpendicular.
Now just use the point slope formula for a line (you know that one, right?)
Do this for another side. Then, solve the two linear equations simultaeously.