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2015-08-24T00:35:31+05:30

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Look at the diagram to derive the formulas.

Radii are :    R1 = 5 cm      R2 = 2 cm
C1 C2 is the distance between the centers.
lengths of direct tangent and transverse tangents are DT and TT respectively.
the formulas are :
     DT² = C1 C2² - (R1 - R2)²   
     TT² = C1 C2² - (R1 + R2)²

Subtract one from the other: 
DT² - TT² = (R1 + R2)² - (R1 - R2)²
             = 4 R1 R2 = 40 cm²    --- (1)
DT = 1.5 TT
=>    (1.5² - 1) TT² = 40      =>  TT² = 32    => TT = 4√2 cm
=>  DT = 6 √2 cm

C1C2² = TT² + (R1 + R2)² = 32 + 49 = 81 cm²

C1 C2  = 9 cm


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