KMO second round #5
Source:
May 6, 2005
geometrycircumcircleincenterratiogeometric transformationgeometry unsolved
Problem Statement
, and are the four different points on the circle in the order. Let the centre of the scribed circle of triangle , which is tangent to , be . Let the centre of the scribed circle of triangle , which is tangent to , be .(1) Show that the circumcentre of triangle is on the circle .(2) Show that the circumcircle of triangle always pass through a fixed point on the circle , when is moving along arc .