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Part of 2016 Germany Team Selection Test

Problems(1)

Easy Geo involving Concyclicity

Source: German TSTST 2016 - #1

7/9/2016
The two circles Γ1\Gamma_1 and Γ2\Gamma_2 with the midpoints O1O_1 resp. O2O_2 intersect in the two distinct points AA and BB. A line through AA meets Γ1\Gamma_1 in C≠AC \neq A and Γ2\Gamma_2 in D≠AD \neq A. The lines CO1CO_1 and DO2DO_2 intersect in XX. Prove that the four points O1,O2,BO_1,O_2,B and XX are concyclic.
Concyclicgeometry unsolvedgeometrycirclecircles