Geometry Chapter 10 Circles Flashcards

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.

Chords and Related Segments

• 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.

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!