Circles Cheat Sheet

Key Definitions

• Circle: A set of points equidistant from a center point. ✅

• Radius (r): Distance from the center to any point on the circle. ✅

• Diameter (d): Distance across the circle through the center. d = 2r ✅

• Circumference (C): The distance around the circle. C = 2πr ✅

• Area (A): The space enclosed by the circle. A = πr² ✅

Important Concepts

Properties of Circles

• Central Angle: An angle whose vertex is the center of the circle.

• Inscribed Angle: An angle formed by two chords in a circle which share an endpoint.

Chord and Arc

• Chord: A line segment with both endpoints on the circle.

• Arc: A part of the circumference of a circle.

Key Formulas

• Circumference: C = 2πr ✅

• Area: A = πr² ✅

• Length of an arc: L = (θ/360) * C (where θ is the central angle in degrees) ✅

• Area of a sector: A_sector = (θ/360) * A ✅

Common Mistakes to Avoid

Common Mistake: Forgetting to convert angles to radians when using trigonometric functions.

Memory Tricks

Tip: "CIRCLE" —

• Circumference

• Is

• Radius

• Chord

• Length of arc

• Enclosed area

Key Diagrams

          O
        /   \
       /     \
     A ------- B
       \     /
        \   /
          C

• O: Center of the circle

• A, B: Points on the circumference

• C: Chord AB

          O
        / | \
       /  |  \
      /   |   \
     A----|----B
          C

• C: Arc AB (part of the circumference)