Circle Theorems: 7 Essential Rules for High School Geometry

Master inscribed angles, subtended chords, cyclic quads, and tangents with diagrams.

Rule 1: Angle at the Center

The angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any point on the circumference.

Rule 2: Angle in a Semicircle (Thales' Theorem)

An angle inscribed in a semicircle where the hypotenuse is the diameter is ALWAYS a right angle (90°).

Rule 3: Angles in the Same Segment

Angles subtended by the same chord or arc in the same circular segment are completely equal.

Rule 4: Opposite Angles of a Cyclic Quadrilateral

The opposite interior angles of any four-sided polygon inscribed in a circle always sum to 180°.

Rule 5 & 6: Tangents and Radius Perpendicularity

A tangent line touches a circle at exactly one point and is perpendicular (90°) to the radius drawn to the point of contact. Two tangents drawn from the same external point are equal in length.