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Parallelograms have two vertices in common [ILL 1974]

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January 2, 2011
geometryparallelogramgeometry proposed

Problem Statement

Let ABCDABCD be an arbitrary quadrilateral. Let squares ABB1A2,BCC1B2,CDD1C2,DAA1D2ABB_1A_2, BCC_1B_2, CDD_1C_2, DAA_1D_2 be constructed in the exterior of the quadrilateral. Furthermore, let AA1PA2AA_1PA_2 and CC1QC2CC_1QC_2 be parallelograms. For any arbitrary point PP in the interior of ABCDABCD, parallelograms RASCRASC and RPTQRPTQ are constructed. Prove that these two parallelograms have two vertices in common.
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