Two circles in the plane intersect at $C$ and $D$. A chord $AB$ of the first circle and a chord $EF$ of the second circle pass through a point on the common chord $CD$. Show that the points $A,B,E,F$ lie on a circle.
Source: Mongolia 1999 Grade 8 P6
Tags: geometry
Two circles in the plane intersect at $C$ and $D$. A chord $AB$ of the first circle and a chord $EF$ of the second circle pass through a point on the common chord $CD$. Show that the points $A,B,E,F$ lie on a circle.