Geometry of Circles

Geometry of Circles

Quick Reference

Contents

5 · Finding measures of Arcs and Angles

10 · Study Guide

1 · Vocabulary

2 · Equation of Circle

6 · Lines in Circles

3 · Central Angles

8 · Areas

4 · Other Angles

Vocabulary

press on each word to get a defintion

Inscribed Angle

Key Terms 1

Circle

Arcs

Central Angle

Diameter

Lines

Key Terms 2

Radius

Circumscribed Angle

Chord

Quizlet Practice

Gimkit Practice: Not Currently Available

Equation of a circle

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

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

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

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

Inscribed Angles

Circumscribed Angles

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

Formed by two chords that intersect on a circle

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

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

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

Central Angles

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**

Finding Arc Length from Central Angle

+CK12 page

Finding measures of arcs and angles

Intersection Inside Circle

Intersection on the Circle

Intersection outside circle

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

To: Inscribed and Circumscribed Angles

Lines in circles

Radius and Chords

Radius and Tangents

2 chords in the same circle

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.

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

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

Diameters and Chords

The above is also true for diameters!

Circumference and Area

Circumference

Area of Circle

Measures the space enclosed by the entire circle

A=πr²

C=2πr

Measures the length around a circle

Area of Sector

Measures the area enclosed by two radii and an arc

Area Sector Central Angle Area Circle 360

Arc Length Central Angle Circumference 360

Arc Length

Measures the length of an arc between two radii.

Extra Practice

Extra Practice Key

Study Guide

Study Guide KEY