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Theorems Of Circles

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Theorems Of Circles

Chapter 10

Mr. Mills

- 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.

- 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.

- 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?

- 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.

- 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

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

#7

Tell why the measure of angle CAM is 28 degrees.

Hint: Think SSS.

- 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.

- # 9
- Explain how to show the length of SC is 21 units.

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

- 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