MathDB

11.3

Part of 2011 All-Russian Olympiad Regional Round

Problems(1)

Rectangle, two circumcircles and centroid

Source: Problem 3 of Russian Regional Olympiad 2011, grade 11

9/1/2011
Point KK lies on the circumcircle of a rectangle ABCDABCD. Line CKCK intersects line segment ADAD at point MM so that AM:MD=2AM:MD=2. OO is the center the rectangle. Prove that the centroid of triangle OKDOKD belongs to the circumcircle of triangle CODCOD. (Author: V. Shmarov)
geometryrectanglecircumcirclegeometry proposed