Cheatography

# Geometry Unit 10 Cheat Sheet (DRAFT) by CCRoses

Holt McDougal Chapter 12

This is a draft cheat sheet. It is a work in progress and is not finished yet.

### Vocabulary

 interior of a circle the set of all points inside the circle exterior of a circle the set of all points outside the circle chord a segment whose endpoints lie in a circle secant a line that intersects a circle at two points tangent a line in the same plane as a cicle that intersects it at exactly one point point of tangency the point where the tangent and a circle intersect is called the point of tangency common tangent a line that is tangent to two circles central angle an angle whose vertex is the center of a circle adjacent arcs arcs of the same circle that intersect at exactly one point congruent arcs two arcs within a circle or two circles that have the same measure sector of a circle a region bounded by two radii of the circle and their interc­epted arc segment of a circle a region bounded by an arc and its chord arc length the distance along an arc measured in linear units inscribed angle an angle whose vertex is on a circle and whose sides contain chords of the circle interc­epted arc consists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them subtends a chord or arc subtends an angle if its endpoints lie on the sides of the angle

### Formulas

 *m = arc measur­ement in degrees* area of a sector of a circle A = 𝜋r2(m/360) area of a segment of a circle A = area of sector - area of the triangle formed inside the sector arc length L = 2𝜋r(m/360)

### Angle Relati­onships in Circles

 vertex of the angle measure of angle on a circle half the measure of its interc­epted arc inside a circle half the sum of the measures of its interc­epted arcs outside a circle half the difference of the measures of its interc­epted arcs

### Angle Relati­onships in Circles

 vertex of the angle measure of angle on a circle half the measure of its interc­epted arc inside a circle half the sum of the measures of its interc­epted arcs outside a circle half the difference of the measures of its interc­epted arcs

### Pairs of Circles

 congruent circles if and only if they have congruent radii concentric circles coplanar circles with the same center tangent circles two coplanar circle that intersect at exactly one point

### Arcs

 minor arc an arc whose points are on or in the interior of a central angle the measure of a minor arc is equal to the measure of its central angle major arc an arc whose points are on or in the eterior of a central angle the measure of a major arc is equal to 360 degrees minus the measure of its central angle semicircle when the endpoints of an arc lie on a diameter the measure of a semicircle is equal to 180 degrees

### Theorems & Postulates

 12-1-1 if a line is tangent to a circle, then it is perpen­dicular to the radius drawn to the point of tangency 12-1-2 if a line is perpen­dicular to a radius of a circle, then the line is tangent to the circle 12-1-3 if two segments are tangent to the same external point, then the segments are congruent 12-2-3 in a circle, if a radius (or diameter) is perpen­dicular to a chord, then it bisects the chord and its arc 12-2-4 in a circle, the perpen­dicular bisector of a chord is a radius (or diameter) 12-4-1 inscribed angle theorem the measure of an inscribed angle is half the measure of its interc­epted arc 12-4-2 if inscribed angles of a circle intercept the same arc or are subtended by the same chord or arc then the angles are congruent 12-4-3 an inscribed angle subtends a semicircle is and only if the angle is a right angle 12-4-4 if a quadri­lateral is inscribed in a circle, then its opposite angles are supple­mentary 12-5-1 if a tangent and a secant (or chord) intersect on a circle at the point of tangency, then the measure of the angle formed is half the measure of its interc­epted arc 12-5-2 if two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its interc­epted arcs 12-5-3 if a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its interc­epted arcs

### Theorem 12-2-2

 in a circle or congruent circles... 1. congruent central angles have congruent chords 2. congruent chords have congruent arcs 3. congruent arcs have congruent central angles