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Triangle ABC has a circumcenter O. What is $\angle AOC,$ in degrees?

 

[asy] unitsize(3 cm);pair A, B, C, O;O = (0,0);A = dir(235);B = dir(160);C = dir(305);draw(A--B--C--cycle);draw(O--A);draw(O--B);draw(O--C);label(

 Apr 12, 2022
 #1
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Angle AOC = 50 degrees

 Apr 12, 2022
 #2
avatar+114 
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very good guest

 Apr 12, 2022
 #3
avatar+124592 
+1

Since O  is the circumcenter  of    ABC,  then   AO = BO = CO =  the circumradius

 

Then angle ABC is an inscribed  angle in the  circumcircle  =  30°

 

But angle AOC  is  a central angle  intercepting  the same arc  as angle ABC

 

So  angle AOC  =  2 * angle ABC  =  2 * 30°  =  60°  

 

cool cool cool

 Apr 12, 2022

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