Circle Theorems

• Angle at the Centre Theorem

  The angle at the centre of a circle is twice the angle at the circumference subtended by the same arc.
• Angle in a Semicircle Theorem

  The angle in a semicircle is a right angle (90°).
• Angles in the Same Segment Theorem

  Angles in the same segment of a circle are equal.
• Cyclic Quadrilateral Theorem

  The opposite angles of a cyclic quadrilateral add up to 180°.
• Tangent and Radius Theorem

  A tangent to a circle is perpendicular to the radius at the point of contact.
• Two Tangents Theorem

  The two tangents drawn from a point outside a circle to the circle are equal in length.
• Alternate Segment Theorem

  The angle between a tangent and a chord is equal to the angle in the alternate segment.
• Perpendicular from Centre to Chord Theorem

  A perpendicular from the centre of a circle to a chord bisects the chord.
• Equal Chords Theorem

  Chords equidistant from the centre of a circle are equal in length.