#### Transcript of Parts of a Circle

Center Point

Radius - Radii

Diameter

Chord

Secant

Tangent

Central Angle

Inscribed Angle

Intersected Arc

Arc major arc - minor arc - semicircle

Theorem --- A line is a tangent if and only if the line is perpendicular to a radius of the circle

Common tangents can be internal or external

The difference is that internal tangents cross through a line that can be drawn from the center of the circle.

Theorem

Tangent Segments from a common external point are congruent

This will be important for the section on special segments

ARCS

Minor Arcs are named with 2 letters, the endpoints, and they lie on the circle. The minor arc is equal to the central angle that shares its endpoints. The sides of the angle that "cuts" a minor arc are radii.

Major Arcs are named with 3 letters, the endpoints and one point on the circle that is between them. This gives reference for the direction you travel to determine the arc's position. They are also 180 degrees of larger. The major arc is equal to 360 - the minor arc.

Semicircles = 180 degrees and are formed by any diameter of a circle. They are named with 3 letters.

Chords

See Theorems 10.3, 10.4, 10.5, 10.6 of the SHS Geometry Book pages 664-666

These four theorems talk about what makes two chords congruent in the same circle or congruent circles.

10.3 of the book matches the "Chords" section on OdysseyWare

Inscribed Angles

An inscribed angle has a vertex on the circle and two endpoints on the circle. Its two sides contain an arc of the circle, this is the intercepted arc.

THEOREM --- The measure of an inscribed angles is equal to 1/2 the measure of its intercepted arc.

THEOREM --- Two inscribed angles that intercept the same arc have congruent angles.

A little more about inscribed angles....

THEOREM --- A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary

The sum of the angles must = 180

**Part one: The IMPACT of Circles **

Parts of a Circle

Arc addition postulate:

The measure of an arc

formed by two adjacent

arcs is the sum of the

measures of the two arcs

THEOREM ---

A semicircle has an

inscribed angle of

90 degrees

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