Circle theorems are fundamental principles in geometry that describe the relationships between angles, lines, and arcs in a circle. These theorems help us understand how different elements, such as chords, tangents, and secants, interact within a circle. For example, one theorem states that the angle formed by two chords intersecting inside a circle is equal to half the sum of the measures of the arcs they intercept. Another important theorem is that the angle formed by a tangent and a chord through the point of contact is equal to the measure of the opposite arc. These theorems are essential for solving various geometric problems and are widely used in mathematics and engineering.