10-3: Arcs & Chords Geometry March 29, 2010. Inscribed & Circumscribed Quad WXYZ is an inscribed polygon because all of its vertices lie on the circle.

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Presentation transcript:

10-3: Arcs & Chords Geometry March 29, 2010

Inscribed & Circumscribed Quad WXYZ is an inscribed polygon because all of its vertices lie on the circle. Circle A is circumscribed about the polygon because it contains all the vertices of the polygon. W X Y Z A

Ex 1: A circle is circumscribed about a regular pentagon. What is the measure of the arc between each pair of consecutive vertices?

Theorem 10.3 If a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc. If BA  TV, then UT  UV and AT  AV. If a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc. If BA  TV, then UT  UV and AT  AV. B C U A TV

Ex 2: Circle W has a radius of 10 cm. Radius WL is  to chord HK which is 16 cm long. a)If HL = 53 , find MK. b)Find JL.

Theorem 10.4 In a circle or in 2  circles, two chords are congruent if and only if they are equidistant from the center.

Ex 3: Chords EF & GH are equidistant from the center. If the radius of circle P is 15 and EF = 24, find PR and RH. EQ F P G R H