Elegance is the key - Part III

Geometry Level 3

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

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