Circles

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Author:
JanineG14
ID:
90355
Filename:
Circles
Updated:
2011-06-20 00:41:50
Tags:
Geometry Circles
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Description:
Geometry (Circles)
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  1. Radius Definition:
    Describes the distance from the center of the circle to the circle itself.
  2. Diameter Definition:
    Describes the distance from one side of the circle to the other side, intersecting the center. Also twice the length of the radius.
  3. Chord Definition:
    A line that connects any two points on a circle. Not necessarily through the center. Note the diameter is a chord.
  4. (pi) =
    3.14 or 22/7
  5. Area of a circle =
    r2
  6. Circumference =
    • 2r or d
    • (d=diameter)
  7. What's the difference b/w a minor & major arc?
    • major arc > 180°
    • minor arc < 180°
  8. What's a central angle?
    any angle whose vertex (point of origin) is at the center of the circle.
  9. What's an inscribed angle?
    any angle whose vertex (point of origin) is on the circumference of a circle.
  10. What is a sector?
    A portion of a circle defined by two radii and an arc carved by a central angle. Can think of as a pizza slice.
  11. Formula for area of a sector?
    • Central Angle * Area of Circle (or πD)
    • 360°
  12. What is a tangent?
    A line that touches a circle at ONLY one point on a circle. It's also perpindicular to the radius at the "point of tangency".
  13. Given the central angle how do you figure out it's corresponding arc?
    The arc in relation to the circumference is the same proportion as the relation of the central angle to the 360°.

    • ex: central angle = 40°
    • 40°/360° = 1/9th
    • so arc = 1/9th of circumference or (1/9th * πD)
  14. What is the formula/relationship b/w central angle & arc?
    • central angle = Minor Arc
    • 360° ______ Circumference
  15. What is the relationship b/w inscribed angles and arcs?
    All inscribed angles that subtend (cut out/create) the same arc are equal in measure.
  16. i.e. if you have three inscribed angles all with the arc AB, then all of the three angles are the same & equal each other.
  17. What is the relationship of Inscribed Angles, Central Angles and Arcs?
    Any inscribed angle that cuts out the same arc as a central angle, is exactly half the measure of that central angle.

    i.e. the central angle is double that of the inscribed angle if they share an arc.
  18. To determine the length of an arc from an inscribed angle you need to...
    Draw in the central angle (which is twice the inscribed angle) and use the arc/central angle proportion to determine the length of the arc.
  19. i.e. can't solve for length of the arc without the central angle.
  20. If you have a circle with diameter endpoints A & B and point C is any point on the circumference of the circle it creates what...
    a Right triangle with C as the right (90°) angle. You can then use rules of triangles in combination with circles to solve problems.
  21. Remember: Difficult geometry questions may require you to find a common shape where one is not explicitly drawn. (ex. equilateral triangle w/ circles).
  22. If each vertex of a polygon is inscribed in the circle, is the polygon inside the circle or around it?
    Polygon is inside circle
  23. If each side of a polygon is tangent to a circle, then the polygon is inside or around the circle?
    The polygon is circumscribed about the circle, thus the circle is inside (inscribed) the polygon.
  24. If a triangle is inscribed in a circle so that one of its sides is a diameter of the circle then the triangle is a...
    right triangle

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