Answer:
a. The length of FA is 1.
b. The length of the radius (AC) is 2.
c. The circumference of the circle A is 4π units.
d. The measure of the minor arc BC is 107°.
e. The length of the minor arc BC is (107/90) π.
f. The m<BFC and m<EFD is 125.5°.
g. The m<BFE is 180°.
Step-by-step explanation:
Radius: R=AB=2
FC=1
Arc CD = 180°
Minor arc BD = 73°
Minor arc EC = 36°
a. What is the length of FA?
FA=AC-FC
AC is a radius, then AC=AB→AC=2
Replacing in the known values in the equation above:
FA=2-1
FA=1
b. What is the length of the radius (AC)?
The radius AC must be equal to the radius AB, then:
AC=AB→AC=2
c. What is the circumference of the circle A?
Circunference of circle A: L=?
L=2 π R
L=2 π (2)
L=4π
d. What is the measure of the minor arc BC?
Minor arc BC = arc CD - Minor arc BD
Minor arc BC = 180°-73°
Minor arc BC = 107°
e. What is the length of the minor arc BC?
Length of minor arc BC: l=?
l=(Minor arc BC / 360°) L
l=(107°/360°) 4π
l=(4*107/360) π
l=(107/90) π
f. What is the m<BFC and m<EFD
<BFC and <EFD are interior angles, then:
m<BFC = m<EFD = ( Minor arc BC + Minor arc DE) / 2
Minor arc DE = arc CD - Minor arc EC
Minor arc DE = 180°-36°
Minor arc DE = 144°
m<BFC = m<EFD = ( 107° + 144° ) / 2
m<BFC = m<EFD = ( 251° ) / 2
m<BFC = m<EFD = 125.5°
g. What is the m<BFE?
<BFE is a straight angle, then m<BFE=180°
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