http://www.ck12.org Chapter 9. Circles
Two arcs arecongruentif their central angles are congruent. The measure of the arc formed by two adjacent arcs is
the sum of the measures of the two arcs (Arc Addition Postulate). An arc can be measured in degrees or in a linear
measure (cm, ft, etc.). In this chapter we will use degree measure.The measure of the minor arc is the same as
the measure of the central anglethat corresponds to it. The measure of the major arc equals to 360◦minus the
measure of the minor arc. In order to prevent confusion, major arcs are always named with three letters; the letters
that denote the endpoints of the arc and any other point on the major arc. When referring to the measure of an arc,
always place an “m” in from of the label.
Example A
FindmAB̂andmADB̂in
⊙
C.mAB̂=m^6 ACB. So,mAB̂= 102 ◦.
mADB̂= 360 ◦−mAB̂= 360 ◦− 102 ◦= 258 ◦Example B
Find the measures of the minor arcs in
⊙
A.EBis a diameter.BecauseEBis a diameter,m^6 EAB= 180 ◦. Each arc has the same measure as its corresponding central angle.
mBF̂=m^6 FAB= 60 ◦
mEF̂=m^6 EAF= 120 ◦→ 180 ◦− 60 ◦
mED̂=m^6 EAD= 38 ◦→ 180 ◦− 90 ◦− 52 ◦
mDĈ=m^6 DAC= 90 ◦
mBĈ=m^6 BAC= 52 ◦Example C
Find the measures of the indicated arcs in
⊙
A.EBis a diameter.a)mF ED̂
b)mCDF̂
c)mDFĈ
Use the Arc Addition Postulate.
a)mF ED̂=mF Ê+mED̂= 120 ◦+ 38 ◦= 158 ◦
b)mCDF̂=mCD̂+mDÊ+mEF̂= 90 ◦+ 38 ◦+ 120 ◦= 248 ◦
c)mDFĈ=mED̂+mEF̂+mF B̂+mBĈ= 38 ◦+ 120 ◦+ 60 ◦+ 52 ◦= 270 ◦
Watch this video for help with the Examples above.
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