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Problems(1)

Prove that APRQ is a parallegoram

Source:

9/9/2010
On the sides of the triangle ABCABC, three similar isosceles triangles ABP (AP=PB)ABP \ (AP = PB), AQC (AQ=QC)AQC \ (AQ = QC), and BRC (BR=RC)BRC \ (BR = RC) are constructed. The first two are constructed externally to the triangle ABCABC, but the third is placed in the same half-plane determined by the line BCBC as the triangle ABCABC. Prove that APRQAPRQ is a parallelogram.
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