Warm-Up

5.

6. 396

Intercepted Arc: An arc that is created by the _______________ of an angle cutting the ____________________.

Central AngleAn angle whose vertex is the ____________ of the circle.

Intercepted Arc Measure:

Inscribed AngleAn angle whose vertex is the ____________ of the circle.

Intercepted Arc Measure:

Central Angle Inscribed Angle

Investigation 1: Chords and Their Central Angles 1.) Draw 2 congruent chords, not diameters,

of any length on your circle.

2.) Connect them to the center to create two radii from each chord

3.) Measure the central angles. What do you notice?

O

Chord Central Angle Conjecture: If two chords in a circle are congruent, then they determine two central angles that are ________________________.

Chord Arcs Conjecture: If two chords in a circle are congruent, then their ________________________ are congruent.

Investigation 2: Tangent Conjectures1.) Draw radius .2.) Draw tangent through T.3.) With your protractor,

measure What do you notice?

Tangent Conjecture: A tangent to a circle is ___________________ to the radius drawn to the point of tangency.

O

OT

AB

OTA and OTB

4.) Draw a second radius, , and another tangent . Make sure the tangents intersect at point B.

5.) Measure . What do you notice?

Tangent Segments Conjecture:Tangent segments to a circle from a point outside the circle are ______________________________.

O

BC OC

TB and CB

Investigation 2: Tangent Conjectures

Tangent Examples

Mixed Review

Homework

Worksheet Packet – Pages 3-4

Homework Review

1. 40 11. 12 ߨ⅓ 1 .1 2. 40 12. 40 2. 6 ହ

ଷߨ

3. 140 180 3. 1ଶଷߨ

4. 180 100 ߨ5 .4 5. 144 13. 90 ߨ ¾ 1 .5 6. 98 55 6. ଼

ଽߨ

7. 49 35 8. 134 14. 50 9. 23 60 10. 49 70

Homework Review

1. x=12 1. 40, 180, 100 3. 90, 55, 35 4. 50, 60, 70