CENTRAL ANGLE

A

B

C

 

AB

C Answer:

A

B

C

D

By Construction:1. Draw a circle with centre C.2. Draw radii AC and BC.3. Measure the angle formed.

• What is the measure of angle ACB?• What is the measure of arc AB?

4. Draw chords AD and BC.5. Measure ADB.

– What is m

A

B

C

D

INSCRIBED ANGLE

An angle whose vertex is on the circle and whose sides are chords of the

circle.

INSCRIBED ANGLE THEOREM

The measure of an inscribed angle is half the measure of

its intercepted arc.

PROOF

Cases:

Case 1Case 2Case 3

Cases:

Case 1Case 2Case 3

Cases:

Case 1Case 2Case 3

Cases:

Case 1Case 2Case 3

EXAMPLE

Case 1:

1.

A

C

O

B

PROVED

Case 2:

= =

=

A C

O

B

DPROVE

D

Case 3:

1. =

2. • • • • =

A

C

O

B

D PROVED

Example:

A

B

CD

In the accompanying figure, mAB=112, mBC=54, and mCD=88. Find m3.

SOLUTION

Solution:mAB + mBC + mCD + mDA = 360 = =27°m2 = mDA = = 53°m3= m 1 + m2 = 27 + 53 = 80° EXERCISE

S

112 + 54 + 88 + mDA = 360mDA = 360m= mBC

Exercises:

1. In O, AC is a diameter, mAD= 70, and m BDC = 30°. Determine the measures of the following:

a. Bb. Cc. BCd. ABe. ADBf. ADC

O

D A

CB

HOMEWORK

Homework:

Given: Quadrilateral ABCD is a rectangle.

Prove: AC and BD are diameters of the circle.

A B

D C

C

DONE

A

B

C

DONE

A

B

C

D

DONE