ABCis a triangle as shown in the diagram below. P, QandRare the midpoints of the sidesBC,CAandABrespectively.Ois the point of intersection of the perpendicular bisectors ofCAandAB.

LetOA=a,OB=bandOC=c.

a) Prove thatOPis perpendicular toBC.

This was pretty straightforward.

b) Hence prove that the perpendicular bisectors of the sides of a triangle are concurrent.

What is this question asking? I'm new to both proofs and vectors, so these types of questions are a challenge.

c) Prove that |a| = |b| = |c|.

As above.

EDIT: Forgot to add the diagram.