The statement provided is correct. If an interval (line segment) subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic, meaning they lie on the same circle.
Here's an explanation of the concept:
1. Consider an interval AB, with A and B as the endpoints.
2. Let P and Q be two points on the same side of AB.
3. Suppose that the angles APB and AQB are equal. This means that the lines AP and AQ or BP and BQ intersect at the same angle.
4. According to the inscribed angle theorem, if two angles in the same segment are equal, then the points defining those angles lie on the same circle.
5. Applying the inscribed angle theorem to the angles APB and AQB, we can conclude that the points A, B, P, and Q are concyclic. This means that they lie on the same circle.
Therefore, if an interval subtends equal angles at two points on the same side of it, the end points of the interval and the two points are concyclic.