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Geometry Level pending

Consider two fixed points $$F'$$ and $$F$$ so that $$F' F = 4$$.

Let $$M$$ be a variable point. Denote $$K$$ and $$L$$ to be the respective orthogonal projections of $$F$$ and $$F'$$ on the bisector of the angle $$F' \hat M F$$.

Assume that $$F' \hat M L = F \hat M K = \alpha$$, and $$FK \times F' L = 3$$. Find $$(MF - MF')^2$$.

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