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MMO 039 Moscow MO 1938 reflections of points in space

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July 18, 2019
geometryreflection3D geometry

Problem Statement

The following operation is performed over points O1,O2,O3O_1, O_2, O_3 and AA in space. The point AA is reflected with respect to O1O_1, the resultant point A1A_1 is reflected through O2O_2, and the resultant point A2A_2 through O3O_3. We get some point A3A_3 that we will also consecutively reflect through O1,O2,O3O_1, O_2, O_3. Prove that the point obtained last coincides with AA..
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