Geometry of Circles

Quick Reference

Geometry of Circles

10 · Study Guide

8 · Areas

6 · Lines in Circles

5 · Finding measures of Arcs and Angles

4 · Other Angles

3 · Central Angles

2 · Equation of Circle

1 · Vocabulary

Contents

press on each word to get a defintion

Key Terms 1

Key Terms 2

Arcs

Lines

Circumscribed Angle

Central Angle

Chord

Inscribed Angle

Radius

Diameter

Gimkit Practice: Not Currently Available

Quizlet Practice

Circle

Vocabulary

(y + k) shift down (y - k) shift up

(x + h) shift left (x - h) shift right

Equation of a circle

(x-h)2 + (y - k)2 = r2

(h, k) is the center of the circle.**Note that the negative sign is part of the equation**

Formed by two tangent lines that intersect outside of the circle.

Intersected Arc = 2 * Inscribed Angle 1/2 Intersected Arc = Inscribed Angle

Inscribed angle of an intersected arc is 1/2 the measure of the angle.

Intersected Arc of an inscribed angle is twice the measure of the angle.

Circumscribed Angles

Formed by two chords that intersect on a circle

Inscribed Angles

Finding Arc Length from Central Angle

Central Angle = Intercepted Arc Measure

A central angle has the vertex at the center of the circle. The arc formed between the legs of the angle is the intercepted arc. **Always use the minor arc unless specifically directed to use the major arc**

Central Angles

+CK12 page

To: Inscribed and Circumscribed Angles

Intersected Arc = 2 * Inscribed Angle 1/2 Intersected Arc = Inscribed Angle

Intersection outside circle

Intersection on the Circle

Intersection Inside Circle

Finding measures of arcs and angles

Radius and Tangents

Lines in circles

Chords are congruent when they are equidistant from the center of the circle.

The above is also true for diameters!

Diameters and Chords

When chords are congruent, their corresponding arcs are congruent.

If a radius and chord intersect at 90 degrees, then the chord is bisected.The intersected arc will also be bisected by the radius.

2 chords in the same circle

Radius and Chords

A tangent line is always perpendicular to the radius through the point of tangency.

Measures the length of an arc between two radii.

Arc Length

Arc Length Central Angle Circumference 360

Area Sector Central Angle Area Circle 360

Measures the area enclosed by two radii and an arc

Area of Sector

A=πr²

Measures the space enclosed by the entire circle

Area of Circle

C=2πr

Measures the length around a circle

Circumference

Circumference and Area

Extra Practice Key

Extra Practice

Study Guide KEY

Study Guide