# Geometry Chapter 10 -10.5

## 40 terms

### circle

set of all points in a plane that are equidistant from a given point

### center

the point that all points on a circle are equidistant to

### radius

a segment whose endpoints are the center and any point on the circle

### chord

a segment whose endpoints are on a circle

### diameter

a chord that contains the center of the circle

### secant

a line that intersects a circle in two points

### tangent

a line, segment, or ray in the plane of a circle that intersects the circle in exactly one point

### point of tangency

the one point where the tangent intersects the circle

### tangent circles

coplanar circles that intersect in one point

### concentric circles

coplanar circles that have a common center

### common tangent

a line, ray, or segment that is tangent to two coplanar circles

### Perpendicular Radius to a Tangent Theorem

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

### Congruent Tangents to External Point Theorem

Tangent segments from a common external points are congruent.

### central angle

an angle whose vertex is the center of the circle

### minor arc

an arc of a circle whose measure is less than 180 degrees

### major arc

an arc of a circle whose measure is more than 180 degrees

### semicircle

an arc with endpoints that are the endpoints of a diameter

### measure of a minor arc

measure of its central angle

### measure of a major arc

360-measure of related minor arc

180

### arc addition postulate

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

### congruent circles

circles with the same radius

### congruent arcs

arcs with the same measure that are part of the same circle or of congruent circles

### Congruent Corresponding Chords and Minor Arcs Theorem

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

### Perpendicular Bisecting Chords & Arcs Theorem

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

### Perpendicular Bisecting Chords & Arcs Converse

If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

### Equidistant Congruent Chords from the Center Theorem

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 arc

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

### Measure of an Inscribed Angle Theorem

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

### Congruent Inscribed Angles with the Same Arc Theorem

If two inscribed angles of a circle intercept the same arc, then the angles are congruent.

### Hypotenuse of an Inscribed Right Triangle is a Diameter Theorem

If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle.

### Hypotenuse of an Inscribed Right Triangle is a Diameter Converse

If one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.

### Supplementary Opposite Angles in an Inscribed Quadrilateral Theorem

A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.

### segments of a chord

when two chords intercept in the interior of a circle, each chord is divided into two segments that are called...

### Segments of a Chord Theorem

If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the products of the lengths of the segments of the other chord.

### Segments of Secants Theorem

If two secant segments share the same endpoint outside a circle, then the product of the lengths of one secant segment and one external segment equals the product of the lengths of the other secant segment and its external segment.

### Segments of Secants and Tangents Theorem

If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segments equals the square of the length of the tangent segment.

### standard equation of a circle

(x-h)² + (y-k)² = r²
Center: (h,k)

x² + y² = r²