Problem
GEO-B2-M08-P011 Angle from the Miquel Point
#11
★★★☆☆ Level 3 of 5
Let \(M\) be the Miquel point of a complete quadrilateral. Prove that \(\angle BMF=\angle BCF\).
Use circle \((BCF)\).
By the definition of the Miquel point, \(M\in (BCF)\). Thus \(B,C,F,M\) lie on one circle, and angles \(\angle BMF\) and \(\angle BCF\) subtend chord \(BF\). Therefore they are equal.
After the Miquel point is found, angles can be read quickly.