Geometry Chapter 10 Review: Circles, Arcs, and Angles

Chord

A line segment with both endpoints on the circle.

Diameter

A chord that passes through the center of the circle, the longest chord.

Tangent

A line that touches the circle at exactly one point.

Secant

A line that intersects the circle at two points.

Minor Arc

An arc that is smaller than a semicircle.

Major Arc

An arc that is larger than a semicircle.

Central Angle

An angle whose vertex is the center of the circle and whose sides are radii.

Inscribed Angle

An angle formed by two chords in a circle which have a common endpoint.

Measure of an Angle

The degree of rotation from one ray to another about their common endpoint.

Measure of an Arc

The degree measure of the central angle that intercepts the arc.

Circumference

The distance around the circle, calculated as C = πd or C = 2πr.

Area of a Circle

The space enclosed by a circle, calculated as A = πr².

Sector

A region of a circle bounded by two radii and the arc between them.

Segment

A region of a circle bounded by a chord and the arc it subtends.

Inscribed Angle Theorem

The inscribed angle is half the measure of the intercepted arc.

Arc Length Formula

The length of an arc is given by (θ/360) * 2πr, where θ is the central angle in degrees.

Area of a Sector Formula

The area of a sector is given by (θ/360) * πr², where θ is the central angle in degrees.

Circle Equation

The equation of a circle in standard form is (x - h)² + (y - k)² = r², where (h, k) is the center.

Radius

A line segment from the center of the circle to any point on the circle.

Concentric Circles

Circles that have the same center but different radii.

Circumscribed Circle

A circle that passes through all the vertices of a polygon.