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In the diagram below, $O$ is the circumcenter of $\triangle ABC$. If $\angle BAC=28^\circ$ and $\angle OAC=32^\circ$, then what is the degree measure of $\angle AOC$?

https://latex.artofproblemsolving.com/d/e/3/de3eeab41d63a04f82bdbeb5b5d702a581fbc004.png

 Oct 29, 2019
 #1
avatar+109740 
+2

Let the intersection  of BO and AC  be  E

 

In triangle ABE....angle BEA  = 90°  angle BAE  =  angle BAC  = 28°

 

So....angle ABE  =  90 - 28  =  62°

 

And  the sum of  angle BAC  +  angle  OAC  =  28 + 32  =  60°

 

Therefore....in triangle BAO....angle AOB  = 180  - 62 - 60  = 58°

 

And by SAS,,,,triangle AEO  is congruent to triangle CEO

 

So...angle AOB  =  angle AOE  = angle COE  =  58°

 

So...angle AOC   =  angle AOE  + angle COE   =  58  + 58   =  116°

 

 

cool cool cool

 Oct 29, 2019
 #2
avatar+117 
+4

Please do not post homework problems; this is considered cheating.


If you need help, then you can use the resources of the online class.

 Oct 30, 2019

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