Bell work Find the value of radius, x, if the diameter of a circle is 25 ft. 25 ft x

Bell work Answer Radius, x, is 12.5 ft

Unit 3 : Circles: 10.2 Arcs and Chords Objectives: Students will: 1. Use properties of arcs and chords to solve problems related to circles.

Words for Circles 1. Central Angle 2. Minor Arc 3. Major Arc 4. Semicircle 5. Congruent Arcs 6. Chord 7. Congruent Chords Check your answers to see how you did. Are there any words/terms that you are unsure of?

Label Circle Parts 1. Semicircles 2. Center 3. Diameter 4. Radius 9. Tangent 10. Secant 11. Minor Arc 12. Major Arc 5. Exterior 6. Interior 7. Diameter 8. Chord

Arcs of Circles CENTRAL ANGLE – An angle with its vertex at the center of the circle Central Angle 60 º CENTER P P A B

Central Angle 60 º CENTER P P A B Arcs of Circles MINOR ARC AB C MAJOR ARC ACB Minor Arc AB and Major Arc ACB

Arcs of Circles Central Angle 60 º CENTER P P A B Measure of the MINOR ARC = the measure of the Central Angle AB = 60 º C The measure of the MAJOR ARC = 360 – the measure of the MINOR ARC ACB = 360 º - 60 º = 300º The measure of the Minor Arc AB = the measure of the Central Angle The measure of the Major Arc ACB = 360º - the measure of the Central Angle 300 º

Arcs of Circles Semicircle – an arc whose endpoints are also the endpoints of the diameter of the circle; Semicircle = 180 º 180 º Semicircle

Arc Addition Postulate The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs AB + BC = ABC 170 º + 8 0º = 2 5 0º A C 170 º 80 º ARC ABC = 250 º B

Example 1 X Y P Z 75 º 110°

Arc Addition Postulate Answers:

(p. 605) Theorem 10.4 In the same circle or in congruent circles two minor arcs are congruent iff their corresponding chords are congruent

Congruent Arcs and Chords Theorem Example 1: Given that Chords DE is congruent to Chord FG. Find the value of x. Arc DE = 100 º Arc FG = (3x +4) º D E FG

Congruent Arcs and Chords Theorem Answer: x = 32 º Arc DE = 100 º Arc FG = (3x +4) º D E FG

Congruent Arcs and Chords Theorem Example 2: Given that Arc DE is congruent to Arc FG. Find the value of x. Chord DE = 25 in Chord FG = (3x + 4) in D E FG

Congruent Arcs and Chords Theorem Answer: x = 7 in Chord DE = 25 in Chord FG = (3x + 4) in D E FG

(p. 605) Theorem 10.5 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chords and its arcs. Diameter Chord P Congruent Arcs Congruent Segments

(p. 605) Theorem 10.6 If one chord is the perpendicular bisector of another chord then the first chord is the diameter Chord 1: _|_ bisector of Chord 2, Chord 1 = the diameter Chord 2 P Diameter

(p. 606) Theorem 10.7 In the same circle or in congruent circles, two chords are congruent iff they are equidistant from the center. (Equidistant means same perpendicular distance) Chord TS  Chord QR __ __ iff PU  VU P Q R S T U V Center P

Example Find the value of Chord QR, if TS = 20 inches and PV = PU = 8 inches P Q R S T U V 8 in Center P

Answer Chord QR = 20 inches (Theroem 10.7)

Home work PWS 10.2 A P (12-46) even

Journal Write two things about Arcs and Chords related to circles from this lesson.