Problem
GEO-B2-M08-P019 Finding the Miquel Point
#19
★★★★☆ Level 4 of 5
Four lines \(l_1,l_2,l_3,l_4\) and the six points \(A,B,C,D,E,F\) of the complete quadrilateral are given. Describe the construction of the Miquel point using only two circles.
Take any two circles of the complete quadrilateral that already share one vertex.
For example, construct circles \((ABE)\) and \((ADF)\). They share point \(A\). Their second intersection \(M\) is the Miquel point. By Miquel's theorem, this point automatically lies on \((BCF)\) and \((CDE)\).
A practical problem: how to actually find the point in a diagram.