Good analytical geometry fromGeometry Level 5
In the figure below,
\(ABCD\) is a square. \(E\) and \(F\) are points on \(BC\) and \(CD\) respectively such that \(AE\) cuts the diagonal \(BD\) at \(G\) and \(FG\) is perpendicular to \(AE\). \(K\) is a point on \(FG\) such that \(AK = EF\). Find the measure of angle \(EKF\) in degrees.