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<CBD=<ADF wanted, pentagon, AE//BC, <ADE = <BDC

Source: 2009 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p7

April 28, 2021
geometrypentagonequal anglesUkraine Correspondence

Problem Statement

Let ABCDEABCDE be a convex pentagon such that AE∥BCAE\parallel BC and ∠ADE=∠BDC\angle ADE = \angle BDC. The diagonals ACAC and BEBE intersect at point FF. Prove that ∠CBD=∠ADF\angle CBD= \angle ADF.
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