Problem
GEO-B2-M08-P002 Six Points of a Complete Quadrilateral
#2
★★☆☆☆ Level 2 of 5
Four lines \(l_1,l_2,l_3,l_4\) meet pairwise, and no three pass through one point. Label the six intersection points and list the four triangles formed by triples of lines.
Go cyclically: neighbouring intersections and two diagonal points.
Let \(A=l_1\cap l_2\), \(B=l_2\cap l_3\), \(C=l_3\cap l_4\), \(D=l_4\cap l_1\), \(E=l_1\cap l_3\), \(F=l_2\cap l_4\). The four triangles are \(ABE\), \(BCF\), \(CDE\), \(ADF\).
It is very important to learn to label the configuration reliably.