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

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

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

Two circles that are tangent to the *same line at the same point*. They may be externally tangent or internally tangent.

**Common Tangent:** A line tangent to two or more circles. They may be externally tangent or internally tangent. *When two circles do not share the same point of tangency but still share a tangent line.*

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.

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

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

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

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

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

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

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

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

Inscribed angles that intercept the same arc are congruent.

Angles inscribed in a semicircle are right angles.

A quadrilateral inscribed in a circle is called a Cyclic Quadrilateral. The two opposite angles in a cyclic quadrilateral add up to 180 degrees.

Parallel lines intercept congruent arcs on a circle.

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

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

Two circles that are tangent to the *same line at the same point*. They may be externally tangent or internally tangent.

**Common Tangent:** A line tangent to two or more circles. They may be externally tangent or internally tangent. *When two circles do not share the same point of tangency but still share a tangent line.*

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.

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

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

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

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

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

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

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

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

Inscribed angles that intercept the same arc are congruent.

Angles inscribed in a semicircle are right angles.

A quadrilateral inscribed in a circle is called a Cyclic Quadrilateral. The two opposite angles in a cyclic quadrilateral add up to 180 degrees.

Parallel lines intercept congruent arcs on a circle.