Problem
GEO-B2-M08-P006 An Ordinary Quadrilateral
#6
★★☆☆☆ Level 2 of 5
In quadrilateral \(ABCD\), lines \(AB\) and \(CD\) meet at \(E\), and lines \(AD\) and \(BC\) meet at \(F\). Which four circles form the Miquel point of the side lines \(AB,BC,CD,DA\)?
Consider the four lines \(AB,BC,CD,DA\).
The triples of these lines give circles \((ABF)\), \((BCE)\), \((CDF)\), and \((DAE)\). They pass through the Miquel point of the complete quadrilateral of the side lines.
Teaches students to see a complete quadrilateral inside an ordinary one.