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The distance between the centers of two circles is 60 cm and their radii are 35 cm and 24 cm. What is the length (in cm) of the direct common tangent to the circles?
  • a)
    √(3479)
  • b)
    61
  • c)
    48
  • d)
    72
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The distance between the centers of two circles is 60 cm and their rad...
We know the formula for length of direct common tangent,
L2 = D2 - (r1 - r2)2
Here L = Length of direct common tangent, D = Distance between the centre of the circles, r1 and r2 are radius of circles,
⇒ L2 = 602 - (35 - 24)2
⇒ L2 = 3600 - 121
⇒ L = (√3479)(3479) cm
∴ Length of direct common tangent = √(3479)
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Most Upvoted Answer
The distance between the centers of two circles is 60 cm and their rad...
Given Data:
- Distance between the centers of two circles: 60 cm
- Radii of the circles: 35 cm and 24 cm

Calculating the Length of the Direct Common Tangent:
- The length of the direct common tangent can be calculated using the formula:
- Length of direct common tangent = √((distance between centers)^2 - (difference in radii)^2)

Plugging in the Values:
- Distance between centers = 60 cm
- Difference in radii = 35 cm - 24 cm = 11 cm
- Length of direct common tangent = √((60)^2 - (11)^2)
- Length of direct common tangent = √(3600 - 121)
- Length of direct common tangent = √3479

Answer:
- The length of the direct common tangent to the circles is √3479 cm, which is option 'A'.
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The distance between the centers of two circles is 60 cm and their radii are 35 cm and 24 cm. What is the length (in cm) of the direct common tangent to the circles?a)√(3479)b)61c)48d)72Correct answer is option 'A'. Can you explain this answer?
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