# 4 3a Central and Inscribed angles by s3dn6csQ

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```									      4.3a: Central/Inscribed Angles
in Circles
p. 452 -458

GSE’s
Primary
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).
Central Angle: an angle whose vertex is at the center of the circle
A
Circle B
ABC         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

80
B
D

Little m indicates degree measure of the arc
C
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.
Major Concept: Degree measures of arcs are the same as its central angles

What is the mFY?

What is the mFRY?
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
In Circle P
m1  140 with diameter AC. Find each measure.
1) m2

2) m BC


3) m AB

4) m ABC
5) mPAB
In circle F, m  EFD = 4x+6, m  DFB = 2x + 20. Find mAB
NECAP Released Item 2009
Inscribed Angle: An angle with a vertex ON the circle and made up of 2 chords

ABC Is the inscribed angle

Intercepted Arc: The arc formed by connecting the two endpoints
of the inscribed angle
Major Concept:

Inscribed angles degree measures are half the degree measure of
their intercepted arc

Ex

What is mACB
What is the mBG

What is the mGCB?
Major Concept:   If 2 different inscribed angles intercept the same arc, then
the angles are congruent

find mACB
and mAGB
Important Fact: If a quadrilateral is inscribed in a circle, then the opposite angles
are SUPPLEMENTARY

What angles are supplementary
Example:
Circle C, mS  28 and mR  110
Find mQ and mT
Find the degree measure
of all angles and arcs
Concentric Circles- circles with the same center, but different Radii

What is an example you can think of outside of geometry?

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