Circles
Basic Terms
- Radius (r): Distance from center to any point on circle
- Diameter (d): d = 2r (longest chord)
- Chord: Line segment joining two points on circle
- Tangent: Line touching circle at one point only
- Secant: Line intersecting circle at two points
- Arc: Part of circumference
- Sector: Region between two radii and an arc
- Segment: Region between chord and arc
Important Formulas
- Circumference: 2πr or πd
- Area: πr²
- Arc length: (θ/360°) × 2πr
- Sector area: (θ/360°) × πr²
- Use π = 22/7 or 3.14
Circle Theorems
- Equal chords are equidistant from center
- Perpendicular from center bisects the chord
- Angle in a semicircle is 90°
- Angles in same segment are equal
- Opposite angles of cyclic quadrilateral = 180°
Tangent Properties
- Tangent is perpendicular to radius at point of contact
- Two tangents from external point are equal
- Angle between tangent and chord = angle in alternate segment
Quick Tips
- Diameter is longest chord
- Only one tangent at a point on circle
- No tangent can be drawn from interior point