Download 13-1 Central and Inscribed

Name ___________________________
Geometry Pd. ___________
13 – 1 Notes
Date _______________
Central and Inscribed Angles in Circles
Today’s Learning Goals: What is a central angle, and what is its relationship with its intercepted arc? What is
an inscribed angle, and what is its relationship with its intercepted arc? What is Thale’s Theorem?
Let’s Prepare for today!
Try to label and identify the following parts you see in this circle
Part of Circle
Radius
Describe it!
Arc
Diameter
Center*
Chord
Flashback! Important Vocabulary/Concepts that we remember…
Major Arc
Minor Arc
Central Angle
Intercepted Arc
*The measure of a central angle and the measure of its intercepted arc are ________________________.
̂ is ___________.
For example, if m∠ABC is 65°, then arc AC is _______ and 𝑚𝐴𝐷𝐶
You try!
̂ = 80,
In circle O, GE is the diameter. If the m𝐺𝐹
Find the m∠GOF
Keep in
mind,
what’s the
arc of a half
circle?
Find the m∠FOE
̂
Find the m𝐹𝐸
̂
Find the m𝐺𝐷𝐸
Turn and Talk
Describe <ABC, how is this different from a central angle?
Inscribed Angle
Let’s watch the simulation – as you watch, are there any notable observations that you can make?
http://www.mathopenref.com/arccentralangletheorem.html
An Inscribed Angle is ________________________________________________________________________________
__________________________________________________________________________________________________
Let's Try It!
Remember to label!
What if… the inscribed angle subtends an arc created by the diameter of the circle?
Sketch:
Let’s watch the simulation – as you watch, are there any notable observations that you can make?
http://www.mathopenref.com/thalestheorem.html
Thale’s Theorem: When an inscribed angle subtends a _______________, the inscribed angle is
a _______ angle.
Talk it out!
With your partner answer the following...
1) What new vocabulary did you learn today?
2) How would you describe any relationships between angles and intercepted arcs in circles?
Name ___________________________
Geometry Pd. ___________
Let's Practice These New Ideas!
1) The circle below has center A.
Identify which intercepted arc goes with
which central angle using the given chart.
2) The circle below has center A.
Identify which intercepted arc goes with
which incribed angle using the given chart.
12 – 1 Practice
Date _______________
3) Given circle with center indicated, find x.
4) Given circle with center indicated,
a) find y
b) find x
c) Explain how you found x and y.
5) Find x:
6) Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 10:2:8.
Determine the size of the angles of the triangle ΔABC. SKETCH YOUR PICTURE!
7) An inscribed angle in a semicircle is a ______________ angle.
9) Find the measure of each arc of Circle P, where RT is a diameter.
̂
a) 𝑅𝑆
̂
b) 𝑅𝑇𝑆
̂
c) 𝑅𝑆𝑇
Name ___________________________
Geometry Pd. ___________
13 – 1 Homework
Date _______________
Directions: Answer the following questions to the best of your ability. Show all work!
*Fill in your road map for today’s lesson!
1. In the accompanying diagram of circle O, the measure of
2. In the accompanying diagram of circle O,
1) 32
2) 48
3) 96
4) 192
3. In the accompanying diagram of circle O,.
1) 210
3) 95
2) 105
4) 75
and
is 38º. What is the measure of
are chords and
What is
. What is
?
?
?
4. Is a diameter a chord? Are all chords diameters? Draw a diagram to defend your answer. Describe the arc which is
made by the diameter of a circle.
5. An angle inscribed in a circle measures 80°. Draw the diagram. What is the number of degrees in the intercepted arc?
6. Chords AB and AC are drawn in circle O. Radii OB and OC are also drawn. Draw the diagram.
Given that m<BAC=50, what is the m<BOC?
7. In the accompanying diagram of circle O,
1) AD CB
≅
3)
2)
4)
and
are diameters. Which statement is not true?
8.
a) How do we know that AB is a diameter based on the markings in the picture?
b) Determine the radius of the circumscribed circle to the right triangle with legs 7 cm and 4 cm. Round to the nearest
hundredth
A recent survey asked teenagers whether they would rather meet a famous musician, athlete, actor, inventor, or other
person. The circle graph shows the results. Find the indicated arc measures:
**Who would you rather meet?