4.1a: Central/Inscribed Angles in Circles

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4.1a Central/Inscribed Angles in Circles
CCSS
GSEs
M(GM)102 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).
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What is a circle?
the set of all points in a plane that are
equidistant from a given point
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Central Angle an angle whose vertex is at the
center of the circle
A
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
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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.
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Major Concept Degree measures of arcs are the
same as its central angles
What is the mFY?
What is the mFRY?
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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
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In Circle P
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In circle F, m EFD 4x6, m DFB 2x
20. Find mAB
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NECAP Released Item 2009
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An angle with a vertex ON the circle and made up
of 2 chords
Inscribed Angle
Is the inscribed angle
The arc formed by connecting the two endpoints
of the inscribed angle
Intercepted Arc
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Major Concept Inscribed angles degree measures
are half the degree measure of their
intercepted arc
Ex
What is
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What is the mBG
What is the mGCB?
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If 2 different inscribed angles intercept the
same arc, then the angles are congruent
Major Concept
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Important Fact If a quadrilateral is inscribed
in a circle, then the opposite angles
are SUPPLEMENTARY
What angles are supplementary
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Example
Circle C,
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Find the degree measure of all angles and arcs
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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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