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GAIC Math 2024 Problem 111

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Given the circle Γ:x2+y2=1\Gamma: x^{2}+y^{2}=1, points A and B are two points symmetric about the x-axis on the circle. M is any point on the circle Γ\Gamma distinct from A and B. If MA and MB intersect the x-axis at points P and Q respectively, then the product of the abscissas of P and Q is _____.

Dataset text MathOdyssey. Open licence.

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