MathDB
AP = PC wanted, circumcircle and 2 midpoints

Source: Mathematics Regional Olympiad of Mexico Center Zone 2018 P2

November 13, 2021
geometryequal segments

Problem Statement

Let △ABC\vartriangle ABCbe a triangle and let Γ\Gamma its circumscribed circle. Let MM be the midpoint of the side BCBC and let DD be the point of intersection of the line AMAM with Γ\Gamma. By DD a straight line is drawn parallel to BCBC, which intersects Γ\Gamma at a point EE. Let NN be the midpoint of the segment AEAE and let PP be the point of intersection of CNCN with AMAM. Show that AP=PCAP = PC.
Back to ProblemsView on AoPS