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Consider a fixed circle \Gamma with three fixed points A, B and C on it. Also, let us fix a real number \lambda \in (0, 1). For a variable points P \notin \{A, B, C\} on \Gamma, let M be the point on the segment CP such that CM = \lambda \cdot CP. Let Q be the second point of intersection of the circumcircles of the triangles AMP and BMC. Prove that as P varies, the point Q lies on a fixed circle.

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