Problem - 04 - National Math Camp 2021 Geometry Test - "Bonus Problem"
Posted: Sun May 09, 2021 4:37 pm
Let $ABC$ be a triangle with circumcircle $(O)$. The midpoints of $BC,CA,AB$ are $A',B',C'$ respectively. The medians $AA', BB', CC'$ cut the circumcircle $(O)$ at $A,A_1; B,B_1; C,C_1$ respectively. The line of tangency to $(O)$ at $A_1$ meets the perpendicular to $AO$ through $A'$ at $X$. Define $Y,Z$ similarly. Prove that $X,Y,Z$ are collinear.