Problem
GEO-B2-M08-P017 Angle Equality in a Quadrilateral
#17
★★★★☆ Level 4 of 5
In quadrilateral \(ABCD\), let \(E=AB\cap CD\), \(F=AD\cap BC\), and let \(M\) be the Miquel point of the side lines. Prove that \(\angle BMF=\angle BCF\) and \(\angle DME=\angle DAE\).
Use circles \((BCF)\) and \((DAE)\).
Since \(M\in (BCF)\), angles \(\angle BMF\) and \(\angle BCF\) subtend chord \(BF\), so they are equal. Since \(M\in (DAE)\), angles \(\angle DME\) and \(\angle DAE\) subtend chord \(DE\), so they are also equal.
Direct practice in reading angles after Miquel.