# What Acute Angle You Have There!

Geometry Level 4

$$ABC$$ is an acute triangle with $$\angle BCA = 35 ^\circ$$. Denote the circumcenter of $$ABC$$ as $$O$$ and the orthocenter of $$ABC$$ as $$H$$. If $$AO=AH$$, what is the value of $$\angle ABC$$ (in degrees)?

Details and assumptions

The circumcenter of a triangle is the center of a circle which passes through all three vertices of a triangle.
The orthocenter of a triangle is the intersection of the 3 altitudes (perpendicular from vertices to opposite side).