Three circles with centers A, B and C have respective

Kelsea Ferry 2022-03-03 Answered
Three circles with centers A, B and C have respective radii 40, 30 and 20 in. and are tangent to each other externally. Find the perimeter of the curvilinear triangle formed by the three circles.
Select one:
a) 94 in
b) 88 in
c) 127 in
d) 134 in
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Expert Answer

Marley Dupont
Answered 2022-03-04 Author has 4 answers
Step 1
PR2=702
RQ2=502
PQ2=602
By cosine law
cosR=PR2+RQ2PQ22(PR)(RQ)
cosR=(70)2+(50)2(60)22(70)(50)
cosR=38007000
R=cos1(3870)57.12
Step 2
By sinc low
sinRPQ=sinQPR
sin57×1260=sinQ70
7060sin57.12=sinQ
Q=sin1(76sin(57.12))78.46
By angle Sum property
mP+mlQ+mlR=180
mP18078.4657.12
mP=44.42
Step 3
Length of arc=Q360×2πr
For arc DF radius =20
and mQ=78.46
Length of arc DF =78.46360×2π(20)
=27.39
For arc DE radius =40
mP=44.42
Length of arc DE =44.42360×2π(40)
=31.01
Step 4
For arc EF
radius (r)=30
mR=57.12
Length of arc EF =57.12360×2π(30)
=29.91
Total perimeter of curvi linear triangle

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