PROBLEM 1

Triangle ABC is an isosceles right triangle with AB = AC = 3. Let M be the midpoint of hypotenuse BC. Points I and E lie on sides AC and AB, respectively, so that AI > AE and AIME is a cyclic quadrilateral. Given that triangle EMI has area 2, the length CI can be written as (a - sqrt(b))/c, where a, b, and c are positive integers and b is not divisible by the square of any prime. What is the value of a + b + c?

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9? 10? 11? 12? 13?

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Cyclic quadrilateral: a quadrilateral whose vertices all lie on a single circle. (inscribed quadrilateral)