MATHS+MATIC= MATHEMATICLES

Geometry Level pending

In triangle ABC, AB = 3, AC = 5, and BC = 7. Let E be the reflection of A over BC, and let line BE meet the circumcircle of ABC again at D. Let I be the incenter of 4ABD. Given that cos2 ∠AEI = m n , where m and n are relatively prime positive integers, determine m + n

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