Question: Let ABC be any triangle with BCA not equal to 120. Let ACP,CBQ be equilateral triangles built on the sides AC,BC outside the triangle ABC.

Let ABC be any triangle with ∠BCA not equal to 120◦. Let ACP,CBQ be equilateral triangles built on the sides AC,BC outside the triangle ABC. Prove that if the points A, B, Q, P lie on a common circle, then |AC| = |BC|.

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