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2023 SSMO Relay Round 3 Problems/Problem 2

Revision as of 21:29, 15 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>T=</math> TNYWR. In triangle <math>ABC</math> with circumradius and inradius having lengths <math>R</math> and <math>r,</math> respectively. Given that...")
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Problem

Let $T=$ TNYWR. In triangle $ABC$ with circumradius and inradius having lengths $R$ and $r,$ respectively. Given that \[\sin\angle{A}+\sin\angle{B}+\sin\angle{C}=\left\{\sqrt{N}\right\}\] the maximum value of \[8\sin\angle{A}\sin\angle{B}\sin\angle{C}\] is $b+c\sqrt{a},$ for squarefree $a,$ find $|a+b+c|.$ (Note that $\left\{x\right\} = x - \lfloor x \rfloor$)

Solution

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