MathDB
2015-2016 Fall OMO #4

Source:

November 18, 2015
Online Math Open

Problem Statement

Let ω\omega be a circle with diameter ABAB and center OO. We draw a circle ωA\omega_A through OO and AA, and another circle ωB\omega_B through OO and BB; the circles ωA\omega_A and ωB\omega_B intersect at a point CC distinct from OO. Assume that all three circles ω\omega, ωA\omega_A, ωB\omega_B are congruent. If CO=3CO = \sqrt 3, what is the perimeter of △ABC\triangle ABC?
Proposed by Evan Chen
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