Paraguayan National Olympiad 2007, Level 3, Problem 5
Source:
September 1, 2014
geometrycircumcircle
Problem Statement
Let be points in the plane, such that we can draw equal circumferences in which the first one passes through and , the second one passes through and , the last one passes through and , and all circumferences share a common point .
Show that the radius of each of these circumferences is equal to the circumradius of triangle , and that is the orthocenter of triangle .