Three circles with centers A, B and C have respective

Kelsea Ferry

Kelsea Ferry

Answered question

2022-03-03

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

Answer & Explanation

Marley Dupont

Marley Dupont

Beginner2022-03-04Added 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

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?