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In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$.  The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle.  If $\angle AOB = 90^\circ$, then find the measure of $\angle MON$, in degrees.

 Apr 11, 2024
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\(Find\ the\ measure\ of\ \angle MON\ in\ degrees.\)

 

\(\angle CAO+\angle CBO=45°\ |\ peripheral\ \angle \ to\ 90°\ (\angle AOB)\\ \angle MON=90°-\angle CAO+90°-\angle CBO\\ =180°-(\angle CAO+\angle CBO)=180°-45°\\ \color{blue}\angle MON=135° \)

 

laugh  !

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 Apr 13, 2024
edited by asinus  Apr 13, 2024

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