# 9.8: Angles Outside a Circle

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central angle

central angle

An angle formed by two radii and whose vertex is at the center of the circle.chord

chord

A line segment whose endpoints are on a circle.diameter

diameter

A chord that passes through the center of the circle. The length of a diameter is two times the length of a radius.inscribed angle

inscribed angle

An angle with its vertex on the circle and whose sides are chords.intercepted arc

intercepted arc

The arc that is inside an inscribed angle and whose endpoints are on the angle.point of tangency

point of tangency

The point where the tangent line touches the circle.Secant

Secant

The secant of an angle in a right triangle is the value found by dividing length of the hypotenuse by the length of the side adjacent the given angle. The secant ratio is the reciprocal of the cosine ratio.Tangent

Tangent

The tangent of an angle in a right triangle is a value found by dividing the length of the side opposite the given angle by the length of the side adjacent to the given angle.Outside Angles Theorem

Outside Angles Theorem

The Outside Angles Theorem states that the measure of an angle formed by two secants, two tangents, or a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs.### Image Attributions

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Description

This concept teaches students how to calculate angles formed outside a circle by tangent and secant lines.

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Date Created:

Jul 17, 2012
Last Modified:

Feb 26, 2015
Vocabulary

central angle

central angle

An angle formed by two radii and whose vertex is at the center of the circle.chord

chord

A line segment whose endpoints are on a circle.diameter

diameter

A chord that passes through the center of the circle. The length of a diameter is two times the length of a radius.inscribed angle

inscribed angle

An angle with its vertex on the circle and whose sides are chords.intercepted arc

intercepted arc

The arc that is inside an inscribed angle and whose endpoints are on the angle.point of tangency

point of tangency

The point where the tangent line touches the circle.Secant

Secant

The secant of an angle in a right triangle is the value found by dividing length of the hypotenuse by the length of the side adjacent the given angle. The secant ratio is the reciprocal of the cosine ratio.Tangent

Tangent

The tangent of an angle in a right triangle is a value found by dividing the length of the side opposite the given angle by the length of the side adjacent to the given angle.Outside Angles Theorem

Outside Angles Theorem

The Outside Angles Theorem states that the measure of an angle formed by two secants, two tangents, or a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs.**Save or share your relevant files like activites, homework and worksheet.**

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