IMO 1974 LL BUL3

Let ABCD be an arbitrary quadrilateral. Let squares ABB1A2,

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IMO 1974 LL BUL3

Origin: BUL

Problem

Let ABCD be an arbitrary quadrilateral. Let squares ABB1A2, BCC1B2, CDD1C2, DAA1D2 be constructed in the exterior of the quadrilateral. Furthermore, let AA1PA2 and CC1QC2 be parallelograms. For any arbitrary point P in the interior of ABCD, parallelograms RASC and RPTQ are constructed. Prove that these two parallelograms have two vertices in common.