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Consider a ΔABC \Delta ABC ΔABC with incentre I I I and circumcircle ω \omega ω. Extend AI‾ \overline {AI} AI such that it meets ω \omega ω at M M M on the other side, as shown in the figure. Given that MI‾=6 \overline {MI} = 6 MI=6 units, find MB‾+MC‾ \overline {MB} + \overline {MC} MB+MC.
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