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Published byAldous McKinney Modified over 8 years ago
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Section 10-3 Inscribed Angles
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Inscribed angles An angle whose vertex is on a circle and whose sides contain chords of the circle. A B D is an inscribed angle.
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Intercepted arc The arc that lies in the interior of an inscribed angle and has endpoints on the angle.
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Measure of an Inscribed Angle Theorem If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc.
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A R T Example: If then m = If m = then =
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An angle inscribed in a semicircle is a right angle. C A T Circle S S Q
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Theorem 10-9 If two inscribed angles intercept the same arc, then the angles are congruent. 2 1
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INSCRIBED Inside another shape CircumSCRIBED Outside another shape
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If all the vertices of a polygon lie on the circle, the polygon is inscribed in the circle and the circle is circumscribed about the polygon.
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When each side of a polygon is tangent to a circle, the polygon is said to be circumscribed about the circle and the circle is inscribed in the polygon.
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If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Theorem 10-10
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D G O Therefore, is a diameter of the circle.
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Theorem 10-11 If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. Q A U D are supplementary are supplementary
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