Problem
GEO-B2-M08-P012 Spiral Centre
#12
★★★☆☆ Level 3 of 5
In a complete quadrilateral, \(M\) is the Miquel point. Prove that \(\angle BME=\angle DMF\) with consistent orientation.
Use circles \((ABE)\) and \((ADF)\).
Since \(A,B,E,M\) are cyclic, \(\angle BME=\angle BAE\). Since \(A,D,F,M\) are cyclic, \(\angle DMF=\angle DAF\). Angles \(\angle BAE\) and \(\angle DAF\) are the same angle between lines \(l_2\) and \(l_1\). Hence \(\angle BME=\angle DMF\).
A connection with the spiral similarity module.