KöMaL 2016 B4834

Let $K$ denote the centre of the circumscribed circle of an acute-angled triangle $ABC$. The line drawn through $K$, parallel to $AB$, intersects line $BC$ at $D$, and line $CA$ at $E$. Similarly, let the line drawn through $K$, parallel to $BC$ intersect line $CA$ at $F$, and line $AB$ at $G$. Prove that the circle of radius $EA$ centred at $E$, the circle of radius $FC$ centred at $F$, and the circumscribed circle of the triangle $ABC$ are concurrent.