10-3: Arcs & Chords

GeometryMarch 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

YZ

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 BATV, then UTUV and ATAV.

B

C

U

A

T V

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.

E QF

P

GR

H