MathDB
<XAD+<XCD=<XBC+<XDC if XA x XC^2 = XB x XD^2, <AXD+<BXC=<CXD

Source: 2021 Saudi Arabia Training Lists p15 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests

January 5, 2022
anglesgeometry

Problem Statement

Let ABCABC be convex quadrilateral and XX lying inside it such that XA⋅XC2=XB⋅XD2XA \cdot XC^2 = XB \cdot XD^2 and ∠AXD+∠BXC=∠CXD\angle AXD + \angle BXC = \angle CXD. Prove that ∠XAD+∠XCD=∠XBC+∠XDC\angle XAD + \angle XCD = \angle XBC + \angle XDC.
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