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Turkish NMO First Round - 2012 Problem - 09 {Geometry}

Source:

July 1, 2012

geometry

Problem Statement

The chord

[CD]

of the circle with diameter

[AB]

is perpendicular to

[AB]

. Let

M

and

N

be the midpoints of

[BC]

and

[AD]

, respectively. If

|BC|=6

and

|AD|=2\sqrt{3}

, then

|MN|=?

<span class='latex-bold'>(A)</span>\ 4 \qquad <span class='latex-bold'>(B)</span>\ 3 \sqrt 2 \qquad <span class='latex-bold'>(C)</span>\ \sqrt{21} \qquad <span class='latex-bold'>(D)</span>\ 5 \qquad <span class='latex-bold'>(E)</span>\ \text{None}

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