MathDB
2016 Latvia National Olympiad 3rd Round Grade12Problem5

Source:

July 22, 2016
functionanalytic geometrygeometry

Problem Statement

Consider the graphs of all the functions y=x2+px+qy = x^2 + px + q having 3 different intersection points with the coordinate axes. For every such graph we pick these 3 intersection points and draw a circumcircle through them. Prove that all these circles have a common point!