Date: Sec 10-2 Concept: Arcs and Chords Objective: Given properties of arcs of a circle, solve for missing angles as measured by a s.g.

Vocabulary: 1.Minor Arc ________ 2.Major Arc _______ 3.Central Angle _______ 4.Semicircle __________ DE DBE <DPE BD

Measure of Minor Arc = Measure of Central Angle Find Each Arc: a.CD _________ b.CDB ________ c.BCD _________

Measure of Minor Arc = Measure of Central Angle Find Each Arc: a.BD _________ b.BED ________ c.BE _________

Thm 10-4: In the same or congruent circles, 2 minor arcs are congruent if and only if their corresponding chords are congruent. AB  BC IFF AB  BC

Example: Find mDC given AD = 3x, DC = x+20 3x X+20 3x= x+20 -x 2x=20 2 X=10 mDC = x+20 =10+20 =30

Thm 10-5: If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc IF PG  DF, Then DE  EF and DG  GF

Thm 10-7: In the same or in congruent circles 2 chords are congruent IFF they are equidistant from the center. AB  CD IFF EG  EF

Example: AB =12, DE =12, CE = 7, Find CG Since CG is  AB, AG  GB Also, CF is  DE, so, DF  FE Also, if AB = DE, then GC=CF Use pyth. Thm to find x, that will also be CG. X = 7 2 X = X 2 = 13 X=3.6

Proof:

Date: Sec 10-3 Concept: Inscribed Angles Objective: Given an inscribed angle, find arc measures as measured by s.g.

Inscribed Angle: An angle whose vertex is on a circle and whose sides contain chords of the circle. Inscribed Angle Intercepted Arc

Example: Find the measure of the angle Measure of Inscribed Angle = ½ the intercepted Arc 80 x X = ½ the arc X=1/2(80) X=40

x = ½ x ½ X=120 Find the measure of the Arc Measure of Inscribed Angle = ½ the intercepted Arc

Example: Find the measure of each arc or angle B A C D mADC = ______ 180 mAC = _______ 70 B A C 140

Find the measure of <BCA m<BCA = ______ 36 B A C 72

Find m<C AB C D M<C = 44

Example:

Proof:

Today’s work