Thinking Cap

Problem of the Month

Congratulations to Sawyer Robertson, winner of the November 2019 Problem of the Month competition!

February 2020

Parallel lines

Given a square \(ABCD\), we take points \(E\) and \(F\) in the interior of the segments \(BC\) and \(CD\), respectively, so that \(\angle EAF = 45^\circ\). The straight lines \(AE\) and \(AF\) intersect the circumscribed circle of the square \(ABCD\) at the points \(G\) and \(H\), respectively. Show that the lines \(EF\) and \(GH\) are parallel.