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equal angles lead to equal ones, related to midpoints of diagonals of trapezoid

Source: 2007 Sharygin Geometry Olympiad Correspondence Round P14

April 27, 2019
geometryequal anglesdiagonalstrapezoid

Problem Statement

In a trapezium with bases ADAD and BCBC, let PP and QQ be the middles of diagonals ACAC and BDBD respectively. Prove that if ∠DAQ=∠CAB\angle DAQ = \angle CAB then ∠PBA=∠DBC\angle PBA = \angle DBC.
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