Difference between revisions of "2023 SSMO Relay Round 3 Problems/Problem 2"
(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== | ==Problem== | ||
| − | Let <math>T=</math> | + | Let <math>T=TNYWR</math>. In triangle <math>ABC</math> with circumradius and inradius having lengths <math>R</math> and <math>r,</math> respectively. Given that |
<cmath>\sin\angle{A}+\sin\angle{B}+\sin\angle{C}=\left\{\sqrt{N}\right\}</cmath> | <cmath>\sin\angle{A}+\sin\angle{B}+\sin\angle{C}=\left\{\sqrt{N}\right\}</cmath> | ||
the maximum value of | the maximum value of | ||
Latest revision as of 19:19, 2 May 2025
Problem
Let 
. In triangle 
with circumradius and inradius having lengths 
and 
respectively. Given that
![\[\sin\angle{A}+\sin\angle{B}+\sin\angle{C}=\left\{\sqrt{N}\right\}\]](http://latex.artofproblemsolving.com/b/9/f/b9f3c666b1307672c54c1ae2d17b8551b7e1f454.png)
the maximum value of
![\[8\sin\angle{A}\sin\angle{B}\sin\angle{C}\]](http://latex.artofproblemsolving.com/a/b/1/ab12aefc00853046c4b1a4e4807e579955d505e9.png)
is 
for squarefree 
find 
(Note that 
)
