Geometry: Unit 10 Circles- Tangents, Chords, Arcs, Angles

Circle

Circle

A set of all points a given distance (radius) from a given point, called the center

Chord

A segment with its endpoints on the circle

Diameter

The longest chord of a circle that always passes through the center

Arc

A continuous portion of between two points on the circle

Semi-circle

An arc that is half a circle, the arc’s endpoints are at the diameter, arc measure is 180°

Minor Arc

An arc that is smaller than semi-circle, the arc measure is less than 180°

Major Arc

An arc that is larger than a semi-circle, the arc measure is greater than 180°

Secant

A line that intersects the circle at exactly two points

Tangent

A line that intersects the circle at exactly one point or touches the circle at 1 point

Sector

An area of circle bounded by two radii and an arc

Tangent Conjecture

A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

Tangent Segment Conjecture

Tangent segments to a circle from a point outside the circle are congruent.

Internally Tangent Circle

Externally Tangent Circle

Common Internally Tangent Circle

Common Externally Tangent Circle

Central Angle

An angle made up of two radius on the circle’s circumference with its vertex at the circle’s center. The measure of the central angle is equal to the measure of its arc.

Inscribed Angle

An angle made up of two chords with its vertex on the circle’s circumference

Chord Central Angles Conjecture

If two chords in a circle are congruent, then they determine two central angles that are congruent.

Chord Arcs Conjecture

If two chords in a circle are congruent, then their intercepted angles are congruent

Perpendicular to a Chord Conjecture

The perpendicular from the center of a circle to a chord is the bisector of the chord

Chord Distance to Center Conjecture

Two congruent chords in a circle are equidistant from the center of the circle

Perpendicular Bisector of a Chord Conjecture

The perpendicular bisector of a chord passes through the center of a circle

Inscribed Angle Theorem

The measure an inscribed angle is half the measure of its intercepted arc

Angle Formed by a Chord and a Tangent Conjecture

The measure of an angle formed by a chord and a tangent is half the measure of its intercepted arc