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Flashcards for McDougal Littell Geometry Chapter 10

### circle

the set of all points in a plane that are equidistant from a given poing, called the center of the circle.

### chord

a segment whose endpoints are on the circle.

### diameter

a chord that passes through a center and the other endpoints is on the circle.

a segment where one endpoint is at the center and the other endpoint is on the circle.

### tangent

a line that intersects a circle at exactly on point.

### point of tangency

the exact point the lines intersects the circle.

### secant

a line that intersects a circle at 2 points

### common tangent

a line that is tangent to 2 circles

### common external tangent

a common tangent that does not intersect the segment that joins the centers of the circles.

### common internal tangent

a common tangent that intersects the segment that joings the centers of the circles.

### concentric

two circles that share the same center.

### congruent circles

two circles that have congruent diameters fo congruent radii.

### theorem 10.1

in a plane, a line is tangent to a cirlce if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.

### theorem 10.2

tangent segments from a common external points are congruent.

### central angle

an angle whose vertex is the center of a circle.

### minor arc

if the measure of angle APB is less than 180 degrees, then the portion of the circle included between points A and B form this

### major arc

this starts and ends with points A and B but it is the arc that lies in the exterior of angle APB.

### semicircle

an arc whose endpoints are the endpoints of a diameter. its measure is always 180.

### measure of a minor arc

is the measure of its central angle.

### measure of a major arc

the difference between 360 and the measure of the related minor arc.

the measure of an arc formed by two adjacent arcs is the sum of the measures of the 2 arcs

### congruent arcs

the arcs are congruent if they have the same measure and they are arcs of the same circle or of congruent circles.

### theorem 10.3

in the same circle, or in congruent circles, 2 minor arcs are congruent if and only if their corresponding chords are congruent.

### theorem 10.4

if one chord is a perpendicular bisector of another chord, then the first chord is a diameter.

### theorem 10.5

if a diameter of a circle is perpendicular to a chord then the diameter bisects the chord and its arcs.

### theorem 10.6

in the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

### inscribed angle

an angle whose vertex is on a circle and whose sides contain chords of the circle.

### intercepted arb

the arc that lies in the interior of an inscribed angle and has endpoints on the angle.

### theorem 10.7

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

### theorem 10.8

if 2 inscribed angles of a circle intercept the same arc, then the angles are congruent.

Example: