Subcontests
(4)system of equations
Let a,b,c be positive real numbers. Find all real solutions (x,y,z) of the system:
ax+by=(x−y)2by+cz=(y−z)2cz+ax=(z−x)2 congruent quadrilaterals
Let ABCD be a cyclic quadrilateral and let HA,HB,HC,HD be the orthocenters of the triangles BCD, CDA, DAB and ABC respectively. Show that the quadrilaterals ABCD and HAHBHCHD are congruent.