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Summary

  •  A circle is the collection of all points in a plane, which are equidistant from a fixed point in the plane.
  •  Equal chords of a circle (or of congruent circles) subtend equal angles at the centre.
  • If the angles subtended by two chords of a circle (or of congruent circles) at the centre (corresponding centres) are equal, the chords are equal.
  • The perpendicular from the centre of a circle to a chord bisects the chord.
  • The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
  • There is one and only one circle passing through three non-collinear points.
  • Equal chords of a circle (or of congruent circles) are equidistant from the centre (or corresponding centres).
  • Chords equidistant from the centre (or corresponding centres) of a circle (or of congruent circles) are equal.
  • If two arcs of a circle are congruent, then their corresponding chords are equal and conversely if two chords of a circle are equal, then their corresponding arcs (minor, major) are congruent.
  • Congruent arcs of a circle subtend equal angles at the centre.
  • The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
  • Angles in the same segment of a circle are equal.
  • Angle in a semicircle is a right angle.
  • If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle.
  • The sum of either pair of opposite angles of a cyclic quadrilateral is
  • If the sum of a pair of opposite angles of a quadrilateral is , the quadrilateral is cyclic.




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