MathDB

3

Part of 1974 IMO Longlists

Problems(1)

Parallelograms have two vertices in common [ILL 1974]

Source:

1/2/2011
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.
geometryparallelogramgeometry proposed