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Geometry Level 3

A triangle AB=3cm, AC=5cm, BC=7cm. Now let E be the reflection of A over BC and let line BE meet circumcircle of triangle ABC again at D. Let I be the incentre of triangle ABD. Given that: Cos^2 (AEI) = m/n. Where m and n are relatively positive prime integers. Then m+n = ?

NOTE: AEI is the angle

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