10-3 Arcs and Chords.

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Presentation transcript:

10-3 Arcs and Chords

Arcs and Chords In a circle (or 2 congruent circles) two minor arcs are congruent if and only if their corresponding chords are congruent. A B C D

Inscribed and Circumscribed Polygons If all the vertices of a polygon lie on a circle then the polygon is inscribed in the circle The circle is circumscribed about the polygon because it contains the vertices B C A E D

Diameters and Chords If a diameter (or radius) is perpendicular to a chord then it bisects the chord and its arc B C T V U A

Example: Circle W has radius 10 cm. Radius WL is perpendicular to chord HK and HK is 16 cm. If mHL = 53, find mMK Find JL M W J H K L

Chords equidistant from the center In a circle, 2 chords are congruent if and only if they are equidistant from the center Example: EF and GH are equidistant form the center. If the radius is 15 and EF=24, Find PR and RH F Q E H P R G

Example: Radius of N is 18, NK=9, mDE=120 Find m<HNE Find HN Find HE Find mGE Y K N X D H E G