Problem
GEO-B2-M08-P009 Full Miquel Theorem
#9
★★★☆☆ Level 3 of 5
Prove that circles \((ABE)\), \((ADF)\), \((BCF)\), \((CDE)\) of a complete quadrilateral have one common point.
Take \(M\) as the second intersection of the first two circles.
Let \(M\) be the second intersection of \((ABE)\) and \((ADF)\). By Problems 7 and 8, point \(M\) also lies on \((BCF)\) and \((CDE)\). Therefore all four circles pass through \(M\).
The central theorem of the module.