Subcontests
(3)Triangle of circumcenters...
Let ABC a acute triangle.
(a) Find the locus of all the points P such that, calling Oa,Ob,Oc the circumcenters of PBC, PAC, PAB:
ABOaOb=BCObOc=CAOcOa
(b) For all points P of the locus in (a), show that the lines AOa, BOb , COc are cuncurrent (in X);
(c) Show that the power of X wrt the circumcircle of ABC is:
−4a2+b2+c2−5R2
Where a=BC , b=AC and c=AB.