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Tangents and
Circumscribed Angles
(Unit 14
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Chord: A segment from
one point on the
circumference to the
another point on the
circumference
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Tangent Line: A line that
intersects a circle at one
point and is perpendicular
to the radius
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The
figure shown to the right is an example of a
tangent angle, formed by the radius and the
tangent line
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Point B is the point of tangency, or where the
tangent line intersects the circle
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All radii in a circle are congruent
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This
means the distance is greater than the
radius
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Two Tangent Theorem

The Two Tangent Theorem states that two
tangent lines that share an endpoint are
congruent
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Proof: The Two Tangent Theorem

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Draw segment DB
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We know these triangles are right
because the radius is perpendicular to
the tangent line
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Segment DB is congruent to segment
DB by the reflexive p
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c
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By CPCTC, the tangent lines are
congruent
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In the
picture to the right, angle ABC is the
circumscribed angle
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Proof: The Circumscribed Angle Theorem

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Angles DAB and DCB are right angles,
since the radii are perpendicular to the
tangent lines
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Figure ABCD is a quadrilateral, so the
angle measures add up to 360 degrees
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Class Quiz
http://mathbitsnotebook
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html

Khan Academy
https://www
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org/math/geometry/hs-geo-circles/
hs-geo-tangents/v/proving-radius-is-perpendicular-to-tangentline



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