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 inb) 88 inc) 127 ind) 134 in

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Marley Dupont · Accepted Answer

Step 1PR2=702RQ2=502PQ2=602By cosine lawcos⁡R=PR2+RQ2−PQ22(PR)(RQ)cos⁡R=(70)2+(50)2−(60)22(70)(50)cos⁡R=38007000R=cos−1(3870)≈57.12∘Step 2By sinc lowsin⁡RPQ=sin⁡QPRsin⁡57×12∘60=sin⁡Q707060sin⁡57.12∘=sin⁡QQ=sin−1(76sin⁡(57.12∘))≈78.46∘By angle Sum propertym∠P+mlQ+mlR=180∘m∠P−180∘−78.46∘−57.12∘m∠P=44.42∘Step 3Length of arc=Q360×2πrFor arc DF radius =20and m∠Q=78.46∘Length of arc DF =78.46∘360×2π(20)=27.39∈For arc DE ⇒ radius =40m∠P=44.42∘Length of arc DE =44.42∘360×2π(40)=31.01∈Step 4For arc EFradius (r)=30m∠R=57.12∘Length of arc EF =57.12360×2π(30)=29.91∈Total perimeter of curvi linear triangle

Three circles with centers A, B and C have respective

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