Subcontests
(4)5 equal circles, intersections of 4 are vertices of a parallelogram
Given convex quadrilateral ABCD inscribed in circle (O,R) (with center O and radius R). With centers the vertices of the quadrilateral and radii R, we consider the circles CA(A,R),CB(B,R),CC(C,R),CD(D,R). Circles CA and CB intersect at point K, circles CB and CC intersect at point L, circles CC and CD intersect at point M and circles CD and CA intersect at point N (points K,L,M,N are the second common points of the circles given they all pass through point O). Prove that quadrilateral KLMN is a parallelogram. x+y+z=xy+yz+zx and xyz=1 , x,y,z>0 with min sum
Find positive real numbers x,y,z that are solutions of the system
x+y+z=xy+yz+zx and xyz=1 , and have the smallest possible sum.