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Find the locus

Source: Oral Moscow geometry olympiad 2023 10-11.2

April 20, 2023
geometry

Problem Statement

Points X1X_1 and X2X_2 move along fixed circles with centers O1O_1 and O2O_2, respectively, so that O1X1∥O2X2O_1X_1 \parallel O_2X_2. Find the locus of the intersection point of lines O1X2O_1X_2 and O2X1O_2X_1.
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