數學vector

Let O be a point inside triangle ABC such that OA^2+BC^2=OB^2+CA^2=OC^2+AB^2

Donate vector OA, OB and OC as a,b and c respectively. Given that AB is perpendicular to OC.

a. If P is a point inside triangle ABC such that vector OP =1/2(a+b+c), show that P is the circumcentre of triangle ABC.

b. Let Q be the centroid of traingle ABC. Show that O, P and Q are collinear.