Ch.10- Circles

Minor Arc

Less than half of the outline of the circle, with measure 0<X<180, named with 2 letters.

Major Arc

More than half of the outline of the circle, with measure 180<X<360, named with 3 letters.

Circumference

The total distance around a circle, calculated with the formula π(d) or πR², where R is the radius.

Central Angle

An angle in a circle where the vertex is at the center of the circle and its measure equals that of its intercepted arc.

Intercepted Arc

Part of a circle created by an angle in a circle, can be major or minor.

Arc Length

The length of an arc in a circle, represented as a fraction of the circumference.

Arc Measure

The measure of an arc in a circle, labeled in degrees, equal to the central angle.

Radian

The measure of a central angle whose intercepted arc’s length equals the radius's length.

Sector

A wedge of a circle whose vertex is the center and includes part of the circumference.

Chord

A segment inside a circle whose endpoints are on the circumference.

Segment of a Circle

Part of the area of the circle created by the chord and its intercepted arc.

Tangent to a Circle

A line that touches the circle at exactly one point and is perpendicular to the radius at that point.

Inscribed Angle

An angle in a circle whose vertex is on the circumference and whose measure is half that of its intercepted arc.

Secant of a Circle

A line that intersects the circle in two points, with its chord being part of the secant.

Arc Measure Calculation Example

The measure of arc ABC is 240 degrees, while its length is a fraction of the circumference.

Area of a Sector

The area of a sector is found by calculating the fraction of the total area of the circle.

Area of a Segment of a Circle

Calculated as sector area minus triangle area using A = (central angle/360) × πr².

Inscribed Angles Theorem

Inscribed angles are half of their intercepted arc, and central angles are equal to intercepted arcs.