MathDB

Triangle

ABC

is an isosceles right triangle with

AB=AC=3

. Let

M

be the midpoint of hypotenuse

\overline{BC}

. Points

I

and

E

lie on sides

\overline{AC}

and

\overline{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

\frac{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

<span class='latex-bold'>(A) </span>9 \qquad <span class='latex-bold'>(B) </span>10 \qquad <span class='latex-bold'>(C) </span>11 \qquad <span class='latex-bold'>(D) </span>12 \qquad <span class='latex-bold'>(E) </span>13 \qquad

Problem Statement