Circle Geometry

Circle Geometry

1. OTHER

   • When two circles touch, their centres and the point of contact are collinear
   • The products of the intercepts of two intersecting chords are equal

2. CHORDS

   • Chords of equal length subtend equal angles at the centre of the circle
   • Equal chords are equidistant from the centre of the circle
   • The perpendicular from the centre of a circle to a chord bisects the chord
     • The perpendicular bisector of a chord passes through the centre of the circle

3. ANGLES

   • Angles in the same segment are equal
   • The angle at the centre is twice the angle at the circumference subtended by the same arc
   • The angle in a semi-circle is a right angle
   • Opposite angles of a cyclic quadrilateral are supplementary

4. SECANTS & TANGENTS

   • The angle between a tangent and radius at the point of contact is 90 degrees
   • The tangents to a circle from an external point are equal in length
   • The angle between a tangent and a chord at the point of contact is equal to the angle in the alternate segment
   • The angle between the tangent and radius at the point of contact is a right angle
   • The product of the intercept of two intersecting secants to a circle from an external point are equal
   • The square of the tangent to a circle from an external point equals the product of the intercepts of any secant from the point