11.1 Angles and Circles Learning Objective: To identify types of arcs and angles in a circle and to...

11.1 Angles and CirclesLearning Objective: To identify types of arcs and angles in a circle and to

find the measures of arcs and angles.

Warm-up (IN)

Notes

Learning Objective: To identify types of arcs and angles in a circle and to find the measures of arcs and angles

Central Angle – Vertex is THE CENTER of the circle

BOCInscribed Angle –

Vertex is ON the circle

BAC Chord –

A segment whose endpoints are on the circle

AB AC


Tangent –

A line, ray or segment that is in the same plane as a circle and intersects it in only one point AND is perpendicular to the radius of the circle

is tangent to circle if

and only if at O.

AC O

AC BO


Arc –

portion of the circle

Semicircle – Half of the circle

ADCMinor Arc –

Less than half of the circle

DC BC AB ADMajor Arc –

More than half of the circle

BAD

Arc Addition Postulate –

mBD mBC mCD

180


Ex 1 – Find the measure of each arc. MN

L

D

K

40

80

a. KM mKM mMN mKN mKM 80

180

mKM 100

b. MNK mMNK mMN mNK mMNK 80 180 260


Measure of a Central Angle –

Equal to the intercepted arc m BOC mBC

Measure of an Inscribed Angle –

Equal to half the intercepted arc

1

2m BAC mBC


Inscribed angles that intercept the same arc are congruent

AFB ADB

The measure of an angle formed by a tangent and a chord is equal to half of the measure of the intercepted arc.

1

2m ABC mAB


Ex 2 – Find the measure of ADB B

CD

A1141

2ADB mAB

mAB m ACB

180m ACB m BCD

m ACB 114 180

m ACB 66

166

2ADB 33

HW –

Out – Describe the difference between an inscribed angle and a central angle and compare their measures.

Summary – Wow, circles are…

11.1 Angles and Circles Learning Objective: To identify types of arcs and angles in a circle and to...

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