intersection of circles (M,ME) and (N,NF) lies on AB
Source: (2021 -) 2022 Dürer Math Competition Regional E+4 https://artofproblemsolving.com/community/c1621671_
November 30, 2022
geometrycollinear
Problem Statement
Let be an acute triangle, and let and be the midpoints of sides and , respectively. Let and be the intersection points of the circle centered at and passing through and the circle centered at and passing through . Prove that if segments and have midpoints and , respectively, then the intersection points of the circle centered at and passing through and the circle centered at and passing through lie on the line .