Difference between revisions of "1982 AHSME Problems/Problem 11"
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Revision as of 12:48, 5 August 2017
Problem 11 Solution
Since 
and 
are angle bisectors of angles 
and 
respectively, $\angleMBO = \angleOBC$ (Error compiling LaTeX. Unknown error_msg) and similarly $\angleNCO = \angleOCB$ (Error compiling LaTeX. Unknown error_msg). Because 
and 
are parallel, $\angleOBC = \angleMOB$ (Error compiling LaTeX. Unknown error_msg) and $\angleNOC = \angleOCB$ (Error compiling LaTeX. Unknown error_msg) by corresponding angles. This relation makes $\bigtriangleupMOB$ (Error compiling LaTeX. Unknown error_msg) and $\bigtriangleupNOC$ (Error compiling LaTeX. Unknown error_msg) isosceles. This makes 
and 
. Therefore the perimeter of $\bigtriangleupAMN$ (Error compiling LaTeX. Unknown error_msg) is 
.
