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Circles: Area, Circumference, Arcs & Theorems

74 cards · 🇺🇸 English

Circle formulas, arcs, chords, sectors and circle theorems.

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Circle

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Cards

  1. 1Circle
    The set of all points in a plane at a given distance (radius) from a given point (center)
  2. 2Center of a circle
    The point equidistant from all points on the circle
  3. 3Radius
    The distance from the center to any point on the circle
  4. 4Diameter
    A line segment passing through the center with endpoints on the circle; twice the radius
  5. 5Relationship between diameter and radius
    Diameter = 2 × radius (d = 2r)
  6. 6Circumference
    The distance around the circle (its perimeter)
  7. 7Formula for circumference
    C = 2πr or C = πd
  8. 8Π (pi)
    An irrational constant approximately equal to 3.14159, the ratio of circumference to diameter
  9. 9What does π equal?
    Approximately 3.14159265... (irrational, never-ending, non-repeating)
  10. 10If a circle has radius 5, what is its circumference?
    10π ≈ 31.42 (C = 2πr = 2π(5))
  11. 11Formula for the area of a circle
    A = πr²
  12. 12If a circle has radius 3, what is its area?
    9π ≈ 28.27 (A = π(3)²)
  13. 13Disc
    The region bounded by a circle (the interior plus the circle itself)
  14. 14Chord
    A line segment whose endpoints lie on the circle
  15. 15Longest chord of a circle
    The diameter
  16. 16Arc
    A connected part of the circle (a portion of the circumference)
  17. 17Semicircle
    Half of a circle, determined by a diameter
  18. 18Sector
    A region bounded by two radii and the arc between them (like a pizza slice)
  19. 19Segment
    A region bounded by a chord and the arc between its endpoints
  20. 20Tangent
    A line that touches the circle at exactly one point
  21. 21The point where a tangent touches a circle
    The point of tangency or point of contact
  22. 22Is a tangent perpendicular to the radius at the point of tangency?
    Yes, always
  23. 23Secant
    A line that intersects the circle at two points
  24. 24Annulus
    A ring-shaped region bounded by two concentric circles
  25. 25Concentric circles
    Circles with the same center but different radii
  26. 26Where does the word 'circle' come from?
    From Greek κύκλος (kuklos) meaning 'ring' or 'hoop'
  27. 27Euclid's definition of a circle
    A plane figure bounded by one curved line such that all straight lines from the center to the boundary are equal
  28. 28Radian
    The angle subtended by an arc whose length equals the radius
  29. 29a full circle → radians
    2π radians (approximately 6.28)
  30. 30a full circle → degrees
    360 degrees

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