Geometry · Trapezoid · Tangential quadrilateral · Pitot theorem · Midline · Tangent circles · Incentre
A circle can be inscribed in the trapezoid \(ABCD\), whose parallel sides are \(AB\) and \(CD\). Prove that the circle having \(BC\) as a diameter and the circle having \(AD\) as a diameter touch each other.
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Serbian National Competition (Drzavno takmicenje) 2010, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source