GeomP1 14.3­14.4 ­ Secants and Secant­Tangent Angles
A Secant is NOT a Chord, Except Sometimes
A secant line is a line that contains a chord of a circle. A secant segment is a segment that contains a chord of a circle.
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Chords:
Secant Lines:
Secant Segments:
Tangents:
GeomP1 14.3­14.4 ­ Secants and Secant­Tangent Angles
Secant Angles
A secant angle is an angle formed by two intersecting secants. C
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It can have its vertex outside the circle.
Secant Angles
A secant angle is an angle formed by two intersecting secants. C
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It can have its vertex inside the circle.
GeomP1 14.3­14.4 ­ Secants and Secant­Tangent Angles
Secant Angles
A secant angle is an angle formed by two intersecting secants. T
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It can have its vertex on the circle.
Secant Angles Theorems
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Interior Secant Angle Measurement Theorem: If a secant angle lies inside the circle, then the measure of the secant angle is ___________________________ ________________________________________________________________.
GeomP1 14.3­14.4 ­ Secants and Secant­Tangent Angles
Secant Angles
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Exterior Secant Angle Measurement Theorem: If a secant angle lies outside the circle, then the measure of the secant angle is ____________________________
________________________________________________________________.
Secant­Tangent Angles
An angle formed by a secant and a tangent is called a secant­tangent angle.
A secant­tangent angle can be outside the circle.
A secant­tangent angle can be on the circle.
Can a secant­tangent angle be inside the circle?
GeomP1 14.3­14.4 ­ Secants and Secant­Tangent Angles
Secant­Tangent Angle Measures
Secant­Tangent Angle Measure Theorem 1: Outside The measure of a secant­tangent angle outside the circle is ______________________________________________.
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Secant­Tangent Angle Measures
Secant­Tangent Angle Measure Theorem 2: On The A
measure of a secant­tangent angle on the circle is ___________________________________________.
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GeomP1 14.3­14.4 ­ Secants and Secant­Tangent Angles
Tangent­Tangent Angle Measures
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A tangent­tangent angle is formed by two tangents.
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Tangent­Tangent Measure Theorem: The measure of a tangent­tangent angle outside the circle is half the difference of the measures of the intercepted arcs.
How could we prove this?