1. Warm up! Find the perimeter of the shaded region.

2. Find the area of the shaded sector.
Practice:
Find the area of the shaded sector. R Q
12 yd

3. Queeeeez time

4. LG 1-3 Circle Theorems

5. Learning goal questions
How are Congruent Chords related?
How does the location of the vertex of an angle effect the formula for finding the angle measure?
When two lines intersect they create an angle. How does the location of the vertex of that angle effect the formula that I will use to find the lengths of those line segments that get created?

6. terminology
Inscribed Angle: an angle whose vertex is on the circle and whose sides contain chords of a circle
Tangent Line: a line in the plane of a circle that intersects a circle at only one point, the point of tangency
Secant Line: a line in the plane of a circle that intersects a circle at exactly two points
Secant Segment: a segment that contains a chord of a circle and has exactly one endpoint outside of the circle
Vertical angles
Linear Pair
Supplementary

7. Secant Line:
intersects the circle at exactly TWO points

8. Tangent Line: a LINE that intersects the circle exactly ONE time
Forms a 90°angle with one radius
Point of Tangency: The point where the tangent intersects the circle

9. Secant Radius Diameter Chord Tangent
Name the term that best describes the notation.
Secant
Radius
Diameter
Chord
Tangent

10. In a circle or in congruent circles, two minor arcs are congruent
Arcs and Chords
Theorem
In a circle or in congruent circles, two minor arcs are congruent
if and only if (iff) their corresponding ______ are congruent.
chords A D
AD  BC
iff B
AD  BC C

11. Warm up
Find the value of x and y.
120 
= 120 x  y
= 60 

12. Graphic Organizer for Angle Theorems

13. Circle P has a radius of 5 units,
and circle T has a radius of 3 units.
If QR = 1, find the following measures: RT PQ AB R P Q T B A

14. The vertices of isosceles triangle ABC are located on circle R.
Arcs and Chords
The vertices of isosceles triangle ABC are located on circle R.
If BA  AC,
identify all congruent arcs. A
BA  AC R C B

15. x = 3 5x = 2x + 9 3x = + 9 In J, m3 = 5x and m 4 = 2x + 9.
Find the value of x.
5x = 2x + 9
3x = + 9
x = 3

16. x = 22 112  1) If measure of JK = 80 and JMK = 2x – 4, find x.
2) If mMKS = 56, find measure of arc MS.
112 

17. Practice and HOMEWORK!