Questions and Answers
What is a circle?
What is the definition of a radius?
A segment with endpoints on the circle
What is the diameter of a circle?
A chord that passes through the center and is made up of collinear radii
What is the diameter formula?
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What is the circumference of a circle?
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What does an inscribed polygon in a circle mean?
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What does circumscribed about a polygon mean?
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What is a chord?
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What is a central angle?
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What is a minor arc?
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What is a major arc?
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What is a semicircle?
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What are congruent arcs?
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What is an intercepted arc?
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What is the Arc Addition Postulate?
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What is the formula for arc length?
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What does it mean if two minor arcs are congruent?
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What happens if a diameter or radius is perpendicular to a chord?
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What defines the perpendicular bisector of a chord?
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What is the significance of equidistant chords in a circle?
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What is an inscribed angle?
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What does the Inscribed Angle Theorem state?
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What does Theorem 10.9 state about inscribed quadrilaterals?
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Study Notes
Circle Definitions and Properties
- A circle is defined as the set of all points in a plane that are equidistant from a central point.
- The radius is a segment from the center to any point on the circle.
- A diameter of a circle passes through the center and is twice the length of the radius, denoted as ( d=2r ).
- Circumference represents the total distance around the circle.
Arcs and Chords
- A chord connects two points on a circle.
- Minor arc is the shorter arc connecting two endpoints, while a major arc is the longer one.
- A semicircle is formed when the endpoints lie on a diameter.
- Congruent arcs have the same measure and are either in the same or congruent circles.
- Adjacent arcs share exactly one common point.
Theorems Related to Circles
- Theorem 10.2 states that in the same circle or congruent circles, two minor arcs are congruent if their corresponding chords are also congruent.
- Theorem 10.3 asserts that a diameter or radius perpendicular to a chord bisects both the chord and its arc.
- Theorem 10.4 indicates that the perpendicular bisector of a chord is a diameter or radius.
- Theorem 10.5 explains that two chords are congruent if they are equidistant from the circle's center.
Inscribed Angles and Intercepted Arcs
- An inscribed angle has its vertex on the circle and its sides are chords of the circle.
- The intercepted arc consists of the arc that lies within an inscribed angle and has endpoints on the angle's sides.
- Inscribed Angle Theorem states that an inscribed angle is half the measure of its intercepted arc.
- Theorem 10.7 claims that if two inscribed angles intercept the same arc or congruent arcs, then those angles are congruent.
- Theorem 10.8 tells that if an inscribed angle intercepts a diameter or semicircle, it measures as a right angle.
Quadrilaterals in Circles
- Theorem 10.9 states that if a quadrilateral is inscribed in a circle, then the sum of its opposite angles equals 180 degrees, indicating they are supplementary.
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Description
This quiz covers essential definitions and properties of circles, including radius, diameter, and circumference. Additionally, it explores the concepts of arcs, chords, and significant theorems related to circles. Test your understanding of these fundamental geometric principles.
