Circles

• Definition and Types
  • Circle: Set of all points in a plane that are at a fixed distance from a fixed point called the centre.
  • Types of Circles: Concentric circles, intersecting circles, tangent circles
• Properties of a Circle
  • Radius: Distance from the centre to any point on the circle
  • Diameter: Longest chord of the circle, twice the radius
  • Circumference: Distance around the circle, calculated as 2 * π * radius
• Chords and Secants
  • Chord: Any line segment joining two points on the circle
  • Secant: A line intersecting the circle at two points
  • Power of a Point: Relationship between the lengths of segments formed by a secant and a tangent
• Tangents and Normals
  • Tangent: A line touching the circle at exactly one point
  • Normal: A line perpendicular to the tangent at the point of contact
  • Properties of Tangents: Length of tangent segment, equal tangents theorem
• Sectors and Arcs
  • Sector: A region enclosed by two radii and an arc
  • Arc: A part of the circumference
  • Measurement of Arcs: Central angle, inscribed angle, angles in the same segment theorem
• Circle Theorems
  • Thales' Theorem: Relationship between the lengths of the sides of a right-angled triangle inscribed in a circle
  • Angle in a Semicircle: Relationship between angles in a semicircle
  • Alternate Segment: Relationship between an angle in a circle and its alternate segment