# Theorems Of Circles - PowerPoint PPT Presentation

1 / 18

Theorems Of Circles. Chapter 10 Mr. Mills. Sum of Central Angles. The sum of the measures of the central agles of a circle with no interior points in common is 360 degrees. Draw circle p with radii PA, PB, PC. The sum of the measures of angles APB, BPC, CPA is 360 degrees. Congruent Arcs.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Theorems Of Circles

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## Theorems Of Circles

Chapter 10

Mr. Mills

### Sum of Central Angles

• The sum of the measures of the central agles of a circle with no interior points in common is 360 degrees.

• Draw circle p with radii PA, PB, PC. The sum of the measures of angles APB, BPC, CPA is 360 degrees.

### Congruent Arcs

• In the same circle or congruent circles, two arcs are congruent if and only if their corresponding central angles are congruent.

• Draw Circle P with radii PA and PB. Draw chord AB.

• Draw an angle CPD that is congruent to central angle APB.

### Congruent arcs

• Draw circle E with congruent angles RED and SET.

• What do you know about Minor arcs RD and ST ?

• If arc ST has a length of 27 inches, what is the length of arc RD?

### Congruent Minor Arcs

• In a circle or congruent circles, two minor arcs are congruent, if and only if their corresponding chords are congruent.

• Draw circle P with chord AB and Chord CD. So that the two chords are congruent.

### Congruent Minor Arcs

• Draw circle E with congruent chords AB and CD.

• What do we know about arcs AB and CD?

• If the measure of arc AB is 56 degrees, what is the measure of arc CD?

• In a circle, if a diameter or radius is perpendicular to a chord, then it bisects the chord and its arc.

• Draw circle P with chord AB and radius CP that is perpendicular to chord AB.

• Draw circle E with radius EZ perpendicular to chord AB. Label the intersection of the chord and radius as point M.

• IF AB has length 10,Find AM and BM

• If AB has length 10 and the radius is 6 find EM, the distance form the center.

M

X

RM = 8

XP = 3

Find MP

R

P

M

X

RX = 12

XP = 5

Find MP

Find XM

Find RM

R

P

### You do the Math

M

X

If RM is congruent to ST , XP is 8, and XM is 6.

Find PS

Find ST

Find Pl

R

P

L

S

T

### Page 543

#7

Tell why the measure of angle CAM is 28 degrees.

Hint: Think SSS.

### Page 543 # 8

• Explain how to show that the measure of arc ES is 100 degrees.

Hint: The sum of interior angles of a triangle is 180 degrees.

### Page 543

• # 9

• Explain how to show the length of SC is 21 units.

### Inscribed Angles

• An inscribed angle is an angle that has its vertex on the circle and its sides contained in chords of the circle.

### Inscribed Angles Theorem

• If an angle is an inscribed angle, then the measure is equal to ½ the measure of the intercepted arc or(the measure of the intercepted arc is twice the measure of the inscribed angle.

• Inscribed angles