1. **Problem Statement:** Identify which angle among \(\angle DOB\), \(\angle BAC\), \(\angle EAC\), and \(\angle ABE\) is an inscribed angle in the given circle. 2. **Definition:** An inscribed angle is an angle formed by two chords in a circle which have a common endpoint on the circle. The vertex of the angle lies on the circle itself. 3. **Analysis of each angle:** - \(\angle DOB\): Formed by points D, O, and B. Since O is the center of the circle, this is a central angle, not an inscribed angle. - \(\angle BAC\): Formed by points B, A, and C. Point A lies on the circle, and B and C are points on or outside the circle. Since the angle vertex is on the circle and the sides are chords, this is a candidate for an inscribed angle. - \(\angle EAC\): Formed by points E, A, and C. Point A is on the circle, E lies on chord AC inside the circle, and C is on the chord. This angle has its vertex on the circle and sides formed by chords, so it is an inscribed angle. - \(\angle ABE\): Formed by points A, B, and E. Point B is on the circle, A is on the circle, and E is inside the circle on chord AC. The vertex is at B, which is on the circle, and the sides are chords, so this is also an inscribed angle. 4. **Conclusion:** Among the options, \(\angle EAC\) is the inscribed angle explicitly described as formed at point A by points E and C on the chord inside the circle. **Final answer:** \(\boxed{\angle EAC}\) is the inscribed angle.