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Transcript 
10.3 presentation.notebook
March 22, 2011
Inscribed Angles
Pg 613
Mar 22­9:02 AM
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10.3 presentation.notebook
March 22, 2011
What Kind of Angle Has a Vertex at
the Center of a Circle?
How do you find the measure of
Arc AC?
Mar 22­9:02 AM
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10.3 presentation.notebook
March 22, 2011
Inscribed angle
• An angle whose vertex is on the circle and whose
sides contain chords of the circle
Inscribed
Angle
Mar 22­9:02 AM
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10.3 presentation.notebook
March 22, 2011
Intercepted Arc
• The arc that lies in the interior of the inscribed
angle and has endpoints on the angle
Intercepted
Arc
Mar 22­9:02 AM
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10.3 presentation.notebook
March 22, 2011
Measure of an Inscribed Angle
• If an angle is inscribed in a circle, then its measure
is half the measure of its intercepted arc
Mar 22­9:02 AM
5
10.3 presentation.notebook
March 22, 2011
Find the measure of the
Intercepted Arc
Mar 22­9:02 AM
6
10.3 presentation.notebook
March 22, 2011
Find the measure of the
Intercepted Arc
Mar 22­9:02 AM
7
10.3 presentation.notebook
March 22, 2011
Find the measure of the Inscribed
Angle
Mar 22­9:02 AM
8
10.3 presentation.notebook
March 22, 2011
Find the measure of Angle ABC
Mar 22­9:02 AM
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10.3 presentation.notebook
March 22, 2011
Theorem 10.9
• If two inscribed angles of a circle intercept the
same arc, then the angles are congruent.
Mar 22­9:02 AM
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10.3 presentation.notebook
March 22, 2011
Find the Measure of the red Angle
Mar 22­9:02 AM
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10.3 presentation.notebook
March 22, 2011
Inscribed and Circumscribed
• Inscribed
• All the vertices of a polygon are on the circle
• Polygon is inscribed
• Circumscribed
• All the vertices of a polygon are on the circle
• Circle is circumscribed
Mar 22­9:02 AM
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10.3 presentation.notebook
March 22, 2011
Angle Inscribed in a Semi­Circle
Mar 22­9:02 AM
13
10.3 presentation.notebook
March 22, 2011
Theorem 10.10
• If a right triangle is inscribed in a circle, then the
hypotenuse is a diameter of the circle.
• Conversely, if one side of an inscribed triangle is a
diameter of the circle, the triangle is a right triangle
and the angle opposite the diameter is the right
angle.
Mar 22­9:02 AM
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10.3 presentation.notebook
March 22, 2011
Find x
Mar 22­9:02 AM
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10.3 presentation.notebook
March 22, 2011
Theorem 10.11
• A quadrilateral can be inscribed in a circle if and
only if its opposite angles are supplementary
Mar 22­9:02 AM
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10.3 presentation.notebook
March 22, 2011
Find y and z
Mar 22­9:02 AM
17
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