Geometry Chapter 10 Circles Flashcards

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Questions and Answers

What is a circle?

A set of all points in a plane that are equidistant from a given point called the center (correct)

A point in the middle of the circle

An angle whose vertex is the center of the circle

A line that intersects a circle in two points

What is the center of a circle?

A point in the middle of the circle making everything equidistant.

What is a radius?

A segment whose endpoints are the center and anywhere else on the circle.

What is a chord?

A segment whose endpoints are on a circle. Signup and view all the answers

What is a diameter?

A chord that contains the center of the circle. Signup and view all the answers

What is a secant?

A line that intersects a circle in two points. Signup and view all the answers

What is a tangent?

A line in the plane of the circle that intersects the circle in exactly one point. Signup and view all the answers

What is a central angle?

An angle whose vertex is the center of the circle. Signup and view all the answers

What defines a minor arc?

The angle formed must be less than 180 degrees. Signup and view all the answers

What defines a major arc?

The points that don't lie on the minor is a major. Signup and view all the answers

What is a semicircle?

An arc with endpoints that are the endpoints of a diameter. Signup and view all the answers

What is the measure of a minor arc?

Measure of the central angle. Signup and view all the answers

What is the measure of a major arc?

The difference between 360 and the measure of the related minor arc. Signup and view all the answers

What are congruent circles?

Must have the same radius. Signup and view all the answers

What are congruent arcs?

If they have the same measure and they are arcs of the same circle or congruent circles. Signup and view all the answers

What is an arc?

An unbroken part of a circle with two points. Signup and view all the answers

What is an inscribed angle?

An angle whose vertex is on a circle and whose sides contain chords of the circle. Signup and view all the answers

What is an intercepted arc?

The arc that lies in the interior of an inscribed angle and has endpoints on the angle. Signup and view all the answers

What is an inscribed polygon?

When all vertices lie on a circle. Signup and view all the answers

What is a circumscribed circle?

If the circle contains the vertices it is. Signup and view all the answers

What are segments of a chord?

When two chords intersect in the interior of a circle, each chord is divided into two segments. Signup and view all the answers

What is a secant segment?

A segment that contains a chord of a circle, and has exactly one endpoint outside the circle. Signup and view all the answers

What is an external segment?

The part of the secant segment that is outside the circle. Signup and view all the answers

Study Notes

Circle Definitions and Properties

A circle is defined as a set of points in a plane that are equidistant from a single point, known as the center.
The center of a circle is the pivotal point from which all points on the circle are equidistant.
The radius of a circle is a line segment from the center to any point on the circle.

A chord is a line segment whose endpoints lie on the circle.
The diameter is a special type of chord that passes through the center, representing the longest distance across the circle.
A secant is a line that intersects the circle at two distinct points, while a tangent only touches the circle at one point known as the point of tangency.

Angles and Arcs

A central angle is formed when the vertex is at the center of the circle, creating two arcs.
A minor arc is defined by an angle that is less than 180 degrees, whereas a major arc encompasses the points not included in the minor arc.
A semicircle is an arc that spans half the circle—its endpoints correspond to the endpoints of a diameter.

Measures of Arcs

The measure of a minor arc corresponds directly to the measure of the central angle that subtends it.
The measure of a major arc is calculated by subtracting the measure of the related minor arc from 360 degrees.

Congruence in Circles

Congruent circles are circles that share the same radius.
Congruent arcs have equal measures and either belong to the same circle or to congruent circles.

Special Angles and Polygons

An inscribed angle has its vertex on the circle and its sides as chords. The associated intercepted arc lies within the inscribed angle, connecting its endpoints.
An inscribed polygon is defined when all those vertices reside on the circumference of the circle. When a circle encompasses the vertices of a polygon, it is referred to as a circumscribed circle.

Chord Segments and Secant Relationships

When two chords intersect within a circle, they create segments that divide each chord into two distinct parts, called segments of a chord.
A secant segment contains a chord of the circle and has one endpoint outside the circle, with the external segment representing the portion of the secant that lies outside the circumference.

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Description

Explore the fundamental concepts of circles in geometry with this set of flashcards. Learn definitions of key terms such as 'circle', 'center', 'radius', and 'chord' to enhance your understanding. Perfect for students studying geometry!