Circle Theorem 1
The angle at the center is twice the angle at the circumference.
Circle Theorem 2
The angle in a semi-cicle is 90°.
Circle Theorem 3
Angles in the same segment are equal.
Circle Theorem 4
Opposite angles in a cyclic quadrilateral add up to 180°.
Circle Theorem 5
The lengths of the two tangents from a point to a circle are equal.
Circle Theorem 6
The angle between a tangent and a radius in a circle is 90°.
Circle Theorem 7
Alternate segment theorem:
The angle (α) between the tangent and the chord at the point of contact (D) is equal to the angle (β) in the alternate segment*.
Circle Theorem 8
Perpendicular from the centre bisects the chord:
Circle Theorems for Arcs and Chords:
- If two chords are congruent, then their corresponding arcs are congruent.
- If the diameter or radius is perpendicular to a chord, then it bisects the chord and its arc.
- In the same circle or congruent circles, two chords are congruent if and only if they are equidistant from the center.