1. The problem is to understand and list all the main circle theorems. 2. Circle theorems are rules about angles, lengths, and arcs in circles that help solve geometry problems. 3. The main circle theorems include: - The angle at the center theorem: The angle subtended at the center of a circle is twice the angle subtended at the circumference by the same arc. - The angle in a semicircle theorem: The angle subtended by a diameter at the circumference is a right angle (90 degrees). - Angles in the same segment theorem: Angles subtended by the same chord and on the same side of the chord are equal. - Opposite angles of a cyclic quadrilateral theorem: The sum of opposite angles in a cyclic quadrilateral is 180 degrees. - The tangent and radius theorem: A tangent to a circle is perpendicular to the radius drawn to the point of contact. - Alternate segment theorem: The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. - The chord bisector theorem: The perpendicular from the center of a circle to a chord bisects the chord. 4. These theorems help find unknown angles and lengths in circle problems by applying the relationships stated. 5. For example, if you know an angle at the center, you can find the angle at the circumference using the first theorem. 6. Remember these theorems as tools to analyze and solve circle geometry problems effectively.