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.