Question

Please help me! 15 points

Answer 1

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°