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2024 SSMO Team Round Problems/Problem 9

Revision as of 15:44, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>ABCDEFGH</math> be an equiangular octagon such that <math>AB=6, BC=8, CD=10, DE=12, EF=6, FG=8, GH=10,</math> and <math>AH=12</math>. The radius of the...")
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Problem

Let $ABCDEFGH$ be an equiangular octagon such that $AB=6, BC=8, CD=10, DE=12, EF=6, FG=8, GH=10,$ and $AH=12$. The radius of the largest circle that fits inside the octagon can be expressed as $a+b\sqrt{c},$ where \(a,b,\) and \(c\) are integers and \(c\) is squarefree. Find $a+b+c.$

Solution

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