Geometry · Geometric construction · Thales circle · Altitudes of a triangle
Let \(M\) and \(N\) be two distinct points, neither of which lies on a given line \(p\). Construct a triangle \(ABC\) whose side \(AB\) lies on \(p\) and for which \(M\) and \(N\) are the feet of the altitudes dropped from \(A\) and from \(B\), respectively.
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Serbian Regional Competition 2009, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source