Problem
GEO-B2-M08-P004 Prove Concyclicity
#4
★★☆☆☆ Level 2 of 5
It is given that \(\angle BMF=\angle BCF\). Prove that points \(B,C,F,M\) lie on one circle.
Use the converse of the inscribed angle criterion.
Angles \(\angle BMF\) and \(\angle BCF\) subtend the same segment \(BF\). Their equality means that points \(M\) and \(C\) lie on one circle with \(B\) and \(F\). Hence \(B,C,F,M\) are concyclic.
A basic converse move.