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