Download 4.3d: Angles from Secants and Tangents

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Transcript 
4.1d: Angles from Secants
and Tangents
CCSS
G-C.2
GSE
Identify and describe relationships among inscribed angles, radii, and chords. Include
the relationship between central, inscribed, and circumscribed angles; inscribed
angles on a diameter are right angles; the radius of a circle is perpendicular to the
tangent where the radius intersects the circle.
http://www.regentsprep.org/Regents/math/geometry/GP15/CircleAngles.htm
Ex.
find mABD
http://www.regentsprep.org/Regents/math/geometry/GP15/CircleAngles.htm
Ex
Find mAFD
chord
A Secant is a line that goes through a circle.
It contains a chord, which is the segment in the circle.
1)
http://www.regentsprep.org/Regents/math/geometry/GP15/CircleAngles.htm
2)
3)
http://www.regentsprep.org/Regents/math/geometry/GP15/CircleAngles.htm
Recap of what the 3 possibilities looks like:
Remember that this theorem only used the intercepted arcs.
Therefore, the red arc in the picture below is not used in this formula.
http://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php
Example
Find x
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm
The End 
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