5.1. The altitudes of triangle $ABC$ intersect at point $O$. It is known that $OC = AB$. Find the angle at vertex $C$.
## 5.1. Answer. $45^{\circ}$.

Let $D$ be the foot of the perpendicular dropped from point $A$. Prove that triangles $C O D$ and $A B D$ are congruent. Then show that $\angle O B D=45^{\circ}$, and from this, deduce that the required angle is also $45^{\circ}$.

Another solution can be obtained by almost verbatim repeating the reasoning presented in the second solution of problem 5.3.