Download U9 Review

Geometry: Unit 9 Review of Circles
S9.1
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S9.2
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S9.3
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I can identify pieces of circles
Circle: The set of ALL points (an infinite number) that are the same
distance away from a central point
 That distance is referred to as the radius
Chord: a line segment with endpoints on the circle
 Diameter: the longest possible chord, runs through
the center
Tangent: a line segment, line or ray that intersects a circle exactly
once
Secant: a line segment, line or ray that intersects a circle exactly
twice
I can solve problems involving central & inscribed angles and their
intercepted arcs
Central angle
o An angle formed with its vertex on the center of the circle
 Is equal to the measure of the intercepted arc it
creates
Inscribed angle
o An angle formed with its vertex on the edge of the circle
 Is equal to half either the central angle or the
intercepted arc
I can solve problems involving intersecting chords and the arcs,
angles and segments created
Chords
o cut each other into 2 pieces each
 product of the pieces is equal
o Create a pair of interior vertical angles, which create 2
unequal intercepted arcs
 The angle is half the sum of the arcs
Geometry: Unit 9 Review of Circles
S9.1
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
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S9.2
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S9.3
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I can identify pieces of circles
Circle: The set of ALL points (an infinite number) that are the same
distance away from a central point
 That distance is referred to as the radius
Chord: a line segment with endpoints on the circle
 Diameter: the longest possible chord, runs through
the center
Tangent: a line segment, line or ray that intersects a circle exactly
once
Secant: a line segment, line or ray that intersects a circle exactly
twice
I can solve problems involving central & inscribed angles and their
intercepted arcs
Central angle
o An angle formed with its vertex on the center of the circle
 Is equal to the measure of the intercepted arc it
creates
Inscribed angle
o An angle formed with its vertex on the edge of the circle
 Is equal to half either the central angle or the
intercepted arc
I can solve problems involving intersecting chords and the arcs,
angles and segments created
Chords
o cut each other into 2 pieces each
 product of the pieces is equal
o Create a pair of interior vertical angles, which create 2
unequal intercepted arcs
 The angle is half the sum of the arcs
Geometry: Unit 9 Review of Circles
S9.4
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S9.5
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S9.7
I can solve problems involving intersecting tangents and the arcs,
angles and segments created
Tangents
o Tangent is perpendicular to radius at point of tangency
o Distance from point of tangency to point of intersection for
2 tangents to the same circle is equal
o Line connecting point of intersection to center of circle is
bisector (creates a kite)
I can solve problems involving intersecting secants and the arcs,
angles and segments created
Secants
o Intersect outside the circle to create an exterior angle and
two unequal intercepted arcs
 The angle is half the difference of the arcs
I can solve problems involving proportions in circles (arc length &
sector area)
Geometry: Unit 9 Review of Circles
S9.4

S9.5
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S9.7
I can solve problems involving intersecting tangents and the arcs,
angles and segments created
Tangents
o Tangent is perpendicular to radius at point of tangency
o Distance from point of tangency to point of intersection for
2 tangents to the same circle is equal
o Line connecting point of intersection to center of circle is
bisector (creates a kite)
I can solve problems involving intersecting secants and the arcs,
angles and segments created
Secants
o Intersect outside the circle to create an exterior angle and
two unequal intercepted arcs
 The angle is half the difference of the arcs
I can solve problems involving proportions in circles (arc length &
sector area)
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Area/Perimeter
o 𝐴 = 𝜋𝑟 2
o 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 2𝜋𝑟
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Area/Perimeter
o 𝐴 = 𝜋𝑟 2
o 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 2𝜋𝑟
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Proportions
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Proportions
o
𝑝𝑎𝑟𝑡
𝑤ℎ𝑜𝑙𝑒
o
𝑎𝑟𝑐 𝑚𝑒𝑎𝑠𝑢𝑟𝑒
360𝑜
o
𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒
360𝑜
=
𝑝𝑎𝑟𝑡
𝑤ℎ𝑜𝑙𝑒
=
𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ
𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒
=
𝑠𝑒𝑐𝑡𝑜𝑟 𝑎𝑟𝑒𝑎
𝐴𝑟𝑒𝑎
o
𝑝𝑎𝑟𝑡
𝑤ℎ𝑜𝑙𝑒
o
𝑎𝑟𝑐 𝑚𝑒𝑎𝑠𝑢𝑟𝑒
360𝑜
o
𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒
360𝑜
=
𝑝𝑎𝑟𝑡
𝑤ℎ𝑜𝑙𝑒
=
𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ
𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒
=
𝑠𝑒𝑐𝑡𝑜𝑟 𝑎𝑟𝑒𝑎
𝐴𝑟𝑒𝑎