VTMO 2026 - Grade 9 - Semifinal - SET 1 - Self-study Question 8

Circles with centres $O,I$ and radii 2,3 respectively intersect at $A,B$, with $\angle AOI=90^\circ$. A secant through $A$ meets the circles again at $M,C$ respectively, with $M,C\ne A$. If $MA=MC$, find $AC$.