MathDB
APx AC = AM xAB + AN x AD.

Source: 2008 Cuba 2.2

August 27, 2024
geometryparallelogram

Problem Statement

Consider the parallelogram ABCDABCD. A circle is drawn that passes through AA and intersects side ADAD at NN, side ABAB at MM and diagonal ACAC in PP such that points A,M,N,PA, M, N, P are different. Prove that AP⋅AC=AM⋅AB+AN⋅AD.AP\cdot AC = AM \cdot AB + AN \cdot AD.
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