10 3 Arcs and Chords Arcs and Chords

10 -3: Arcs and Chords

Arcs and Chords • The endpoints of a chord are also the endpoints of an arc. • In a circle, if two minor arcs are congruent, then their chords must be congruent as well. In the following figures are arc AB and arc CD congruent? EX 1: Quad ABDC is a rectangle. EX 2:

Circles and Polygons • The inscribed shape is on the inside. • The circumscribed shape is on the outside.

Circumscribed or Inscribed? EX 1: Triangle LMN is _______ in circle O. EX 2: Circle O is _________ about triangle LMN. EX 3: Circle P is _________ about the polygon. EX 4: Octogon QRSTUVWX is an ___________.

Determine the measure of each arc. EX 1: EX 2:

Diameters and Chords If a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc.

EX 1: Find AY. EX 2: Find AD. EX 3: Find YD. EX 4: Find DB. EX 5: Find AB.

Example 3 on p. 538 in textbook • Circle O has a radius of 13 in. Radius OB is perpendicular to chord CD, which is 24 in. long. • A. If m. CD = 134, find m. CB. • B. Find OX.

Additional. Ex. 3 from TE textbook Circle W has a radius of 10 cm. Radius WL is perpendicular to chord HK, which is 16 cm long. a. If m. HL = 53, find m. MK. b. Find JL

If circle A has a radius of 5, CD=4, and AF=3, find AC, BD, and EG. Two chords are congruent if and only if they are equidistant from the center.

A chord of a circle is 48 cm long and is 10 cm. from the center of the circle. Find the radius.

Assignment Regular: p. 540 + 541: 11 -35 odd, 40 -41 W. S. 10 -3: 1 -14 Honors : p. 540 + 541: 11 -35, 40 -41 W. S. 10 -3: 1 -14