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Circumcircles with a common point

Source: Moldova NMO 2002 grade 10 problem nr.8

November 3, 2008
geometrycircumcircle

Problem Statement

Let the triangle ADB1 ADB_1 s.t. m(∠DAB1)≠90∘ m(\angle DAB_1)\ne 90^\circ.On the sides of this triangle externally are constructed the squares ABCD ABCD and AB1C1D1 AB_1C_1D_1 with centers O1 O_1 and O2 O_2, respectively.Prove that the circumcircles of the triangles BAB1 BAB_1, DAD1 DAD_1 and O1AO2 O_1AO_2 share a common point, that differs from A A.
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