# Geometry Circle Theorems

version from 2015-06-19 00:01

## Section

CircleA set of all points in a plane equidistant from a given point called the center.
Arc Addition PostulateThe measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.
If a line is tangent to a circle...then the line is perpendicular the radius at the point of tangency.
If a line in a plane of a circle is perpendicular to a radius at its endpoint on the circle...then the line is tangent to a circle.
If two tangent segments to a circle share a common endpoint outside the circle...then the two segments are congruent.
(central angles, arcs) In a circle or in congruent circles... (Regular)congruent central angles have congruent arcs
(central angles, arcs) In a circle or in congruent circles... (Converse)congruent arcs have congruent central angles.
(central angles, chords) Within a circle or congruent circles... (Regular)congruent central angles have congruent chords.
(central angles, chords) Within a circle or congruent circles... (Converse)congruent chords have congruent central angles.
(chords, arcs) Within a circle or in congruent circles... (Regular)congruent chords have congruent arcs.
(chords, arcs) Within a circle or in congruent circles... (Converse)congruent arcs have congruent chords.
(chords equidistant) Within a circle or in congruent circles... (Regular)chords equidistant from the center or centers are congruent.
(chords equidistant) Within a circle or in congruent circles... (Converse)congruent chords are equidistant from the center (or centers).
(parallel chords) In a circle, or in congruent circles... (Regular)parallel chords intercept congruent arcs between them.
(parallel chords) In a circle or congruent circles... (Converse)congruent arcs are intercepted by parallel chords.
In a circle, if a diameter is perpendicular to a chord...then it bisects the chord and its arc.
In a circle, if a diameter bisects a chord...then it is perpendicular to the chord.
In a circle, the perpendicular bisector of a chord contains...the center of the circle.
The measure of an inscribed angle is...one half the measure of its intercepted arc.
Two inscribed angles that intercept the same arc are...congruent.
An angle inscribed in a semicircle is...a right angle.
The opposite angles of a quadrilateral inscribed in a circle are...supplementary.
The measure of an angle formed by a tangent and a chord is...half the measure of the intercepted arc.
The measure of each angle formed by two lines that intersect inside a circle is...one half the sum of the measures of the intercepted arcs.
The measure of an angle formed by two lines that intersect outside a circle is...half the difference of the measures of the intercepted arcs.
For a given point and circle...the product of the lengths of the two segments from the point to the circle is constant along any line through the point and the circle.
Case 1: ab = cdThe products of the chord segments are equal.
Case 2: w(w+x) = y(y+z)The products of the secants and their outer segments are equal.
Case 3: t^2 = y(y+z)The product of the secant and its outer segment equals the square of the tangent.