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Unformatted text preview: 145 Inscribed Angles and Intercepted Arcs
A) An angle is inscribed in an arc if 1. the sides of the angle contain the end points of the arc and 2. the vertex of the angle is a point, but not an end point, of the arc B) An angle intercepts an arc if 1. the end points of the arc lie on the angle 2. all other points of the arc are in the interior of the angle, and 3. each side of the angle contains an end point of the arc C) Theorem 1416 (The Inscribed Angle Theorem) a. The measure of an inscribed angle is half the measure of its intercepted arc b. Proof (case 1) ( The angle contains a diameter of the circle) c. (case 2) (the arc endpoints are on opposite sides of the diameter) d. (case 3) (the arc endpoints are on the same side of the diameter) D) Corollary 1416.1 a. Any angle inscribed in a semicircle is a right angle E) Corollary 1416.2 a. Every two angles inscribed in the same arc are congruent F) Inscribed a. A triangle is inscribed in a circle if the vertices of the triangle lie on the circle. Inscribed triangle G) Circumscribed about a. If each side of the quadrilateral is tangent to the circle, then the quadrilateral is circumscribed about the circle Circumscribed triangle (number 14 from the hw) Prove the following theorem The opposite angles of an inscribed quadrilateral are supplementary.
H) 1) 1) 2) 3) 2) 3) I) (number 16 from the homework) In semicircle ACB, at D. Prove that CD is the geometric mean of AD and DB. 1) Introduce 2) 3) 1) 2) 3) ...
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 Spring '09
 Johnson
 Algebra, Arc, Inscribed Angle Theorem, circle Circumscribed triangle

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