Geometry - Circles

• Radius


  A segment joining the center and a point on the circle. (The plural form of radius is radi. All radii are equal.)
• Diameter


  A segment that passes through the center and each endpoint is on the circle. (Diameter is twice the radius)
• Chord


  A segment that joins two points on a circle. (A diameter is also considered as a chord.)
• Secant


  A segment, ray, or line that contains a chord.
• Tangent


  A line that intersects the circle in one point.
• Arc


  A portion or part of the circle lying between two points of the circle
• Types of arcs


  • Semicircle (an arc that measures exactly 180 degrees)
  • Minor Arc (an arc that measures more than 0 degrees, but less than 180 degrees)
  • Major Arc (an arc that measures more than 180 degrees, but less than 360 degrees)
• Central Angle


  Equal to its intercepted arc. The point is in the center.
• Inscribed Angle


  Half of the intercepted arc. The angle is formed by two points on the circle's circumference.
• Inscribed Circle


  Each side of the polygon is equal to the circle.
• Circle Theorems


  • Angles intercepting the same arc are equal
  • Radius-Tangent Theorem (The line tangent to the circle is perpendicular to the radius drawn to the point of tangency. This forms a right triangle, which makes it possible to solve using the Pythagorean Theorem)
  • Tangent-Tangent Theorem (Two tangent segments to a circle that meet an external point are congruent)
  • Congruent chords have congruent arcs (Vice-versa)
  • The diameter is perpendicular to a chord
  • Radius/Diameter - Chord Theorem (If the diameter is perpendicular to a chord, then it bisects the chord and its arc)
  • Distance of 2 Chords from the Center (Congruent chords are equidistant from the center, Vice-versa)