Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2023 SSMO Relay Round 3 Problems/Problem 2

Revision as of 22:29, 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...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2023_SSMO_Relay_Round_3_Problems/Problem_2&oldid=207680"