Let O and H be the circumcenter and orthocenter of acute triangle ABC, respectively. If angle AHC + angle AOC = 240 degrees, what is the measure of angle ABC in degrees?


I've tried splitting the triangles into isoceles triangles, but i just got stuck and I genuinely have no clue how to solve the problem from this point.

Any help?

Im not exactly sure what the relationship is between the three angles mentioned above.

 Nov 19, 2022
edited by oDivis  Nov 19, 2022

Unless I have made a mistake with my drawing I do not think there is a set answer to this question.


I have two different sketches here that both match the data given and angle ABC has 2 diferent values. 


Namely 50 degrees and  48 degrees.  I suppose the answers are close. Maybe it is rounding error in the construction.


Angle ABC will always be a half of angle AOC though.   

(The angle at the centre is twice the angle at the circumference when botha standing on the same arc )


Here is a link to the interactive diagram.    https://www.geogebra.org/classic/gdpx2ktn



 Nov 19, 2022
edited by Melody  Nov 19, 2022

Thanks for your answer!

oDivis  Nov 21, 2022

4 Online Users