1. 4.1a: Central/Inscribed Angles in Circles
CCSS:
GSE’s
M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem).

2. What is a circle? the set of all points in a plane that
are equidistant from a given point

3. Central Angle: an angle whose vertex is at the center of the circle
Circle B
Has a vertex at the center B C
Sum of Central Angles:
The sum of all central angles in a circle
Is 360 degrees. A
Find m 80 B D
Little m indicates degree measure of the arc C

4. AC is a minor arc. Minor arcs are less than 180 degrees. They use the
the two endpoints.
ADC is a major arc. Major arc are greater than 180 degrees. They use three letters, the endpoints and a point in-between them.

5. Major Concept: Degree measures of arcs are the same as its central angles
What is the mFY?
What is the mFRY?

6. NECAP type question
Circle P has a diameter added to its figure every step
so all central angles are congruent.
What is the sum of the measures of 3 central angles after
the 5th step? Explain in words how you know.
Step 2
Step 1
Step 3

7. In Circle P

8. In circle F, m EFD = 4x+6, m DFB = 2x + 20. Find mAB

9. NECAP Released Item 2009

10. Inscribed Angle:
An angle with a vertex ON the circle and made up of 2 chords
Is the inscribed angle
Intercepted Arc:
The arc formed by connecting the two endpoints
of the inscribed angle

11. Major Concept:
Inscribed angles degree measures are half the degree measure of
their intercepted arc Ex
What is

12. What is the mBG
What is the mGCB?

13. If 2 different inscribed angles intercept the same arc, then
the angles are congruent
Major Concept:

14. Important Fact: If a quadrilateral is inscribed in a circle, then the opposite angles
are SUPPLEMENTARY
What angles are supplementary

15. Example:
Circle C,

16. Find the degree measure
of all angles and arcs

18. Concentric Circles- circles with the same center, but different Radii
What is an example you can think of outside of geometry?