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2023 WSMO Team Round Problems/Problem 9

Revision as of 15:37, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== A circle has three chords of equal length, <math>4 + 2 \sqrt{3}</math> which intersect forming a triangle with side lengths 2, 2, and <math>2 \sqrt{3}</math>. If...")
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Problem

A circle has three chords of equal length, $4 + 2 \sqrt{3}$ which intersect forming a triangle with side lengths 2, 2, and $2 \sqrt{3}$. If the radius of the circle is $r,$ then $r^2 = a-b\sqrt{c},$ for positive integers $a,b$ and squarefree $c.$ Find $a+b+c.$

Solution

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