Triangle ABC has a circumcenter O. What is

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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(

Guest Apr 12, 2022

Guest · Answer 1 · 2022-04-12T02:50:09

Angle AOC = 50 degrees

Kakashi · Answer 2 · 2022-04-12T05:55:47

very good guest

CPhill · Answer 3 · 2022-04-12T06:34:45

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°