Find \(\angle BAC\).

Let's analyze the problem step by step. 1. We are given a circle with center O. A line AC is tangent to the circle at point A. Point B lies on the circle, and segment AB is a chord. 2. We need to find the measure of \(\angle BAC\). 3. Notice that the radius OA is perpendicular to the tangent AC at the point of tangency A. This means that \(\angle OAC = 90^{\circ}\). 4. Also, it appears that \(\angle OAB = \angle BAC\), this means that \(\angle OAB = 45^{\circ}\). 5. Then, \(\angle BAC = \angle OAC - \angle OAB\). 6. \(\angle BAC = 90^{\circ} - 45^{\circ} = 45^{\circ}\). So \(\angle BAC\) is 45 degrees. Answer: 45°