Triangle $\triangle{ABC}$,O=circumcenter of (ABC),OA=R,the A-excircle intersect (AB),(BC),(CA) at points F,D,E. If the A-excircle has radius R prove that $OD\perp EF$
Source: Second Romanian JBMO TST 2016
Tags: geometry
Triangle $\triangle{ABC}$,O=circumcenter of (ABC),OA=R,the A-excircle intersect (AB),(BC),(CA) at points F,D,E. If the A-excircle has radius R prove that $OD\perp EF$