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Questions and Answers
What is the definition of a chord in relation to a circle?
What is the definition of a chord in relation to a circle?
How is the diameter of a circle defined?
How is the diameter of a circle defined?
What does the Central Angle-Intercepted Arc Postulate state?
What does the Central Angle-Intercepted Arc Postulate state?
What defines a tangent to a circle?
What defines a tangent to a circle?
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How can arc length be calculated?
How can arc length be calculated?
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What is the relationship between the measure of an arc and the angle that intercepts it?
What is the relationship between the measure of an arc and the angle that intercepts it?
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Which statement best describes an inscribed angle?
Which statement best describes an inscribed angle?
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What does the Arc Addition Postulate state?
What does the Arc Addition Postulate state?
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Study Notes
Circle Definitions
- Circle: The set of all points equidistant from a fixed point (center).
- Center: The fixed point from which all points on the circle are equidistant.
- Radius: A line segment connecting the center to a point on the circle.
- Diameter: A line segment passing through the center and connecting two points on the circle.
- Chord: A line segment connecting two points on the circle.
- Central Angle: An angle formed by two radii with its vertex at the center of the circle.
- Inscribed Angle: An angle formed by two chords sharing an endpoint on the circle.
- Arc: A portion of the circumference of a circle.
- Secant: A line that intersects a circle at two distinct points.
- Tangent: A line that touches the circle at only one point and does not enter the circle.
Theorems and Postulates
- Central Angle - Intercepted Arc Postulate: The measure of a central angle is equal to the measure of its intercepted arc (and vice versa).
- Arc Degree Measure: Half the measure of the circle.
- Arc Addition Postulate: The measure of an arc formed by two adjacent arcs is the sum of the measures of those arcs.
- Arc Length Formula: (arc degree measure/360) * 2πr
- Segments Perpendicular to a Chord Theorem: If a diameter or radius is perpendicular to a chord, then it bisects the chord and its arc.
Additional Information
- GCF (Greatest Common Factor) values: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
- Diameter is a special type of chord.
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Description
This quiz covers essential definitions and theorems related to circles in geometry. You'll explore concepts such as radius, diameter, chords, and various types of angles, as well as important postulates. Test your understanding of these foundational terms and relationships.
