Difference between revisions of "1991 IMO Problems/Problem 5"
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− | {{ | + | Let <math>\A_{1}</math> , <math>\A_{2}</math>, and <math>\A_{3}</math> = <math>\measuredangle CAB</math>, <math>\measuredangle ABC</math>, <math>\measuredangle BCA</math>, respcetively. |
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+ | Let <math>\alpha_{1}</math> , <math>\alpha_{2}</math>, and <math>\alpha_{3}</math> = <math>\measuredangle PAB</math>, <math>\measuredangle PBC</math>, <math>\measuredangle PCA</math>, respcetively. | ||
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+ | {{alternate solutions}} |
Revision as of 11:11, 12 November 2023
Problem
Let be a triangle and
an interior point of
. Show that at least one of the angles
is less than or equal to
.
Solution
Let $\A_{1}$ (Error compiling LaTeX. Unknown error_msg) , $\A_{2}$ (Error compiling LaTeX. Unknown error_msg), and $\A_{3}$ (Error compiling LaTeX. Unknown error_msg) = ,
,
, respcetively.
Let ,
, and
=
,
,
, respcetively.
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.