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ASU 006 All Russian MO 1961 9.1a 10.4b equilateral

Source:

June 17, 2019
geometryEquilateralLocus

Problem Statement

a) Points AA and BB move uniformly and with equal angle speed along the circumferences with OaO_a and ObO_b centres (both clockwise). Prove that a vertex CC of the equilateral triangle ABCABC also moves along a certain circumference uniformly.
b) The distance from the point PP to the vertices of the equilateral triangle ABCABC equal ∣AP∣=2,∣BP∣=3|AP|=2, |BP|=3. Find the maximal value of CPCP.
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