Download Chapter 10: Circles

Chapter 10: Circles
Objective: I will review and
apply theorems related to
circles
10.1 Circles and
Circumference
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Name a circle by the letter at the center of the circle
Diameter- segment that extends from one point on
the circle to another point on the circle through the
center point
Radius- segment that extends from one point on
the circle to the center point
Chord- segment that extends from one point on the
circle to another point on the circle
Diameter=2 x radius (d=2r)
Circumference: the distance around the circle

C=2πr or
C= πd
10.2 Angles, Arcs and Chords
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10.2
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Semi-circle: half the circle (180 degrees)
Minor arc: less than 180 degrees
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Major arc: more than 180 degrees
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Name with two letters
Name with three letters
Minor arc = central angle
Arc length: arc  2r
360
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Find x and angle AZE
10.3 Arcs and Chords
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If two chords are congruent, then their arcs
are also congruent
In inscribed quadrilaterals, the opposite
angles are supplementary
If a radius or diameter is perpendicular to a
chord, it bisects the chord and its arc
If two chords are equidistant from the center
of the circle, the chords are congruent
A
If FE=BC, then arc FE =
arc BC
B
Quad. BCEF is an
inscribed polygon –
opposite angles are
supplementary
F
angles B + E = 180 &
angles F + C = 180
C
E
D
Diameter AD is
perpendicular to chord EC
– so chord EC and arc EC
are bisected
Find the radius
10.4 Inscribed Angles
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Inscribed angle: an angle inside the circle
with sides that are chords and a vertex on
the edge of the circle
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Inscribed angle = ½ intercepted arc
An inscribed right angle, always intercepts a
semicircle
If two or more inscribed angles intercept the
same arc, they are congruent
A. Find mX.
Refer to the figure. Find the measure of
angles 1, 2, 3 and 4.
ALGEBRA Find mI.
ALGEBRA Find mB.
The insignia shown is a quadrilateral inscribed in
a circle. Find mS and mT.
10.5 Tangents
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Tangent: a line that shares only one point
with a circle and is perpendicular to the
radius or diameter at that point.
Point of tangency: the point that a tangent
shares with a circle
Two lines that are tangent to the same circle
and meet at a point, are congruent from that
point to the points of tangency
10.6 Secants, Tangents, and
Angle Measures
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Secant and Tangent
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Two Secants:
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Interior angle = ½ (sum of intercepted arcs)
Two Secants
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Interior angle = ½ intercepted arc
Exterior angle = ½ (far arc – close arc)
Two Tangents
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Exterior angle = ½ (far arc – close arc)
A. Find x.
B. Find x.
C. Find x.
A. Find mQPS.
B.
A.
B.
10.7 Special Segments in a
Circle
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Two Chords
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Two Secants
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seg1 x seg2 = seg1 x seg2
outer segment x whole secant =
outer segment x whole secant
Secant and Tangent
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outer segment x whole secant = tangent squared
*Add the segments to get the whole secant
A. Find x.
B. Find x.
Find x.
LM is tangent to the circle. Find x. Round to the
nearest tenth.
Find x. Assume that segments that appear
to be tangent are tangent.
EXIT TICKET
Find x.
HOMEWORK
P620 (1-15 odd, 17-20, 28-33, 41, 44,
47, 50)