chapter 12 circles vocab. circle – the set of all points in a plane a given distance away from a...
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Chapter 12
Circles Vocab
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Circle – the set of all points in a plane a given distance away from a center
point.
A
A circle is named by its center point. For example: Circle
A or A.
Radius – the “given distance away from the center point” of a circle; a segment that joins the center to a
point on the circle.
Radius (r) Plural: Radii
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Sphere – the set of all points a given distance away from a center
point.
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Chord – a segment whose endpoints lie on on the circle.
Example: DC
A BC
D
Diameter – a chord that passes through the center of the circle. Example: AB
A diameter is twice the length of a radius.
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Secant – a line that contains a chord.
Example: ABA
B
**Note: A chord and a secant can be named using the same letters. The
notation tells you whether it is a secant or a chord. A secant is a line; a chord is a
segment.**
Secant: AB Chord: AB
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Tangent – a line that intersects a circle at exactly one point.
Not a tangent
!
A
B
The point at which the circle and the tangent intersect is called the
point of tangency.
Example: AExample: AB
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Section 12 - 1
Tangents
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Theorem 12-1: If a line is tangent to a circle, then the line is
perpendicular to the radius drawn to the point of tangency.
If AB is tangent to Circle Q at point C, then QC
AB.A BC
Q
Q is the center of the circle. C is a point of tangency.
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Example: Given Circle Q with a radius length of 7. D is a point of tangency. DF = 24, find the length of QF.
FD
Q
7
24
72 + 242 = QF2
QF = 25
Extension: Find GF.
G
QG = 7QF = 25 GF = 18
NOTE: G is NOT
necessarily the midpoint
of QF!!
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Theorem 12-2: If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the
circle.
This is the converse of Theorem 12-1.
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Theorem 12-3: IF two tangent segments to a circle share a
common endpoint outside the circle, then the two segments are
congruent.
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Common Tangent – a line that is tangent to two coplanar
circles.Common Internal Tangent
Intersects the segment joining the centers.
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Common External Tangent
Does not intersect the segment joining the
centers.
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Tangent Circles – coplanar circles that are tangent to the same line at the same point.
Internally Tangent Circles Externally
Tangent Circles
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Congruent Circles – circles with
congruent radii.5cm
5cm
Concentric Circles – circles with the same center point.
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When each side of a polygon is tangent to a circle, the circle is said to be inscribed in the polygon.
This circle is inscribed
inside of the pentagon.
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When each vertex of a polygon is on the circle, the circle is said to be circumscribed around the polygon.
This circle is circumscribed
around the pentagon