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

Consider a triangle ABC.

Since AB and AC are intersecting line segments,so we can say that their right bisectors must also intersect.

Let them meet in P (say)

We know that every point the right bisector of a segment is equidistant from the end points.

So,

 AP=PC  (i)...(P lies on the right bisector of AB)

and

AP=PC..(ii) (as P lies on the right bisector of AC)

from (i) and (ii)

 BP=PC

Thus, we can say that P lies on the right bisector of BC, as it's equidistant from B and C.

 Thus we see that P lies on the right bisectors of all therr sides of the triangle.

 Thus , proved.

This question can be done by taking any of the two sides of the triangle in the beginning. Method remains the same.