MathDB

4

Part of 2016 Regional Olympiad of Mexico Center Zone

Problems(1)

vertex of # AMPN is circumcenter of ABC, starting with 2 intersecting circles

Source: Mathematics Regional Olympiad of Mexico Center Zone 2016 P4

11/12/2021
Let AA be one of the two points where the circles whose centers are the points MM and NN intersect. The tangents in AA to such circles intersect them again in BB and CC, respectively. Let PP be a point such that the quadrilateral AMPNAMPN is a parallelogram. Show that PP is the circumcenter of triangle ABCABC.
geometrycirclesCircumcenterparallelogram