InterviewSolution
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InterviewSolution
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The radii of the two circles are 6 cm & 8 cm respectively. The distance between the center of the two circles is 15 cm, then find the ratio of the length of the direct common tangent to the length of the transverse common tangent.1. √321 ∶ √292. √221 ∶ √193. √221 ∶ √294. √121 ∶ √29 |
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Answer» Correct Answer - Option 3 : √221 ∶ √29 GIVEN: The radii of the two circles R1 = 6 cm & R2 = 8 cm respectively and the distance between the center of the two circles(C1C2) = 15 cm FORMULA USED: Length of direct common tangent = √(C1C2)2 - (R1 - R2)2 & Length of the transverse tangent = √(C1C2)2 - (R1 + R2)2 CALCULATION: R1 = 6 cm & R2 = 8 cm and C1C2 = 15 cm ⇒ Length of direct common tangent = √(C1C2)2 - (R1 - R2)2 ⇒ √(C1C2)2 - (R1 - R2)2 = √(15)2 - (8 - 6)2 ⇒ √225 - 4 ⇒ √221 cm Length of the transverse tangent = √(C1C2)2 - (R1 + R2)2 ⇒ √(15)2 - (8 + 6)2 ⇒ √225 - 196 ⇒ √29 cm ⇒ the ratio of the length of the direct common tangent to the length of the transverse common tangent = √221 ∶ √29 ∴ The ratio of the length of the direct common tangent to the length of the transverse common tangent = √221 ∶ √29 |
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