# Geo2.39

From Example Problems

Prove that the perpendicular bisectors of the sides of a triangle are concurrent.

Let be the vertices of the triangle ABC.

If D,E,F are the midpoints of the sides respectively,then

Slope of BC is

Therefore,slope of the perpendicular bisector to the side is

Equation to the perpendicular bisector thro'D is

Simplifying, we have

Similarly the other perpendicular bisectors are

Now implies are concurrent.

Hence the required is proved.