# Mystery Triangle

Geometry Level 5

Triangle $$X_1X_2X_3$$ has $$X_1X_2=1$$. Circles $$\Gamma_1$$, $$\Gamma_2$$, and $$\Gamma_3$$ are drawn such that $$\Gamma_i$$ has center $$X_i$$ and passes through $$X_{i+1}$$ ($$\Gamma_3$$ passes through $$X_1$$).

Given that $$\Gamma_1$$ is internally tangent to $$\Gamma_2$$ at $$P$$, and $$\Gamma_3$$ also passes through $$P$$, then find the value of $$(X_1X_2\cdot X_2X_3\cdot X_3X_1)^2$$

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