Podcast
Questions and Answers
In the same circle, or in congruent circles, two chords are congruent if and only if they are _________________ from the center.
In the same circle, or in congruent circles, two chords are congruent if and only if they are _________________ from the center.
equidistant
A __________ is an angle whose sides are tangent to a circle.
A __________ is an angle whose sides are tangent to a circle.
circumscribed
A(n) _______ angle is an angle whose vertex is on the circle, and whose sides contain chords of the circle.
A(n) _______ angle is an angle whose vertex is on the circle, and whose sides contain chords of the circle.
inscribed
A ______ angle is an angle whose vertex is at the center of the circle.
A ______ angle is an angle whose vertex is at the center of the circle.
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A _________ is the set of all points in a plane equidistant from a given point.
A _________ is the set of all points in a plane equidistant from a given point.
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Two circles with the same center are called ____________ circles.
Two circles with the same center are called ____________ circles.
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An arc of a circle with a measure of 180 degrees is a ____________.
An arc of a circle with a measure of 180 degrees is a ____________.
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A _______ arc of a circle has a measure of less than 180 degrees.
A _______ arc of a circle has a measure of less than 180 degrees.
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A _______ arc of a circle has a measure of more than 180 degrees.
A _______ arc of a circle has a measure of more than 180 degrees.
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A polygon is an inscribed polygon when all its ________ are on the circle.
A polygon is an inscribed polygon when all its ________ are on the circle.
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An arc that lies between two lines, rays, or segments is called an _____ arc.
An arc that lies between two lines, rays, or segments is called an _____ arc.
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Tangent segments from a common exterior point are _______.
Tangent segments from a common exterior point are _______.
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A(n) _______ segment is the part of a secant segment that is outside the circle.
A(n) _______ segment is the part of a secant segment that is outside the circle.
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A quadrilateral can be inscribed in a circle if and only if its opposite angles are _________.
A quadrilateral can be inscribed in a circle if and only if its opposite angles are _________.
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Two circles are ________ if and only if they have the same radius.
Two circles are ________ if and only if they have the same radius.
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If one side of an inscribed triangle is a _______ of a circle, then the triangle is a right triangle.
If one side of an inscribed triangle is a _______ of a circle, then the triangle is a right triangle.
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Study Notes
Circle Theorems and Definitions
- Two chords in the same or congruent circles are congruent if they are equidistant from the center.
- A circumscribed angle has sides that are tangent to a circle.
- An inscribed angle has its vertex on the circle, with sides that contain chords of the circle.
- A central angle has its vertex at the center of the circle.
Circle Properties
- A circle is defined as the set of all points in a plane that are equidistant from a given point (the center).
- Circles that share the same center are referred to as concentric circles.
- An arc measuring 180 degrees is known as a semicircle.
Types of Arcs
- A minor arc measures less than 180 degrees.
- A major arc measures more than 180 degrees.
- An intercepted arc lies between two lines, rays, or segments.
Inscribed Polygons and Quadrilaterals
- A polygon is inscribed in a circle if all its vertices lie on the circle.
- A quadrilateral can be inscribed in a circle only if its opposite angles are supplementary.
Segments and Congruence
- Tangent segments drawn from a common external point to a circle are congruent.
- An external segment of a secant is the part that lies outside the circle.
Triangle Properties in Circles
- An inscribed triangle is a right triangle if one of its sides is a diameter of the circle.
- Two circles are congruent if they have the same radius.
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Description
This quiz focuses on key concepts from Chapter 10 of Geometry, including definitions related to chords, angles, and circles. Use this review to reinforce your understanding of terms like 'equidistant', 'circumscribed', and 'inscribed'. Perfect for preparing for tests or exams in geometry.
