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AD x BC = AB x DC + BD x AN - 2012 Cuba MO 2.6

Source:

September 18, 2024
geometry

Problem Statement

Let ABCABC be a right triangle at AA, and let ADAD be the relative height to the hypotenuse. Let NN be the intersection of the bisector of the angle of vertex CC with ADAD. Prove that AD⋅BC=AB⋅DC+BD⋅AN.AD \cdot BC = AB \cdot DC + BD \cdot AN.
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