What Acute Angle You Have There!
\(ABC\) 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).
You may choose to read this page on extended sine rule.