Geometry · Cyclic quadrilateral · Tangential quadrilateral · Pitot theorem · Locus of constant angle · Ruler and compass construction
Three points \(A\), \(B\), \(C\), not lying on one line, are given. Construct a point \(D\) for which the quadrilateral \(ABCD\) is at the same time cyclic and tangential, that is, admits both a circumscribed circle through its four vertices and an inscribed circle touching all four of its sides.
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Serbian National Competition (Drzavno takmicenje) 2007, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source