Multiple choice

What will be the distance between centre of two circles having radius of 19cm and 10cm? Length of direct common tangent is given as 12cm .

  1. 15cm

  2. 20cm

  3. 19cm

  4. 10cm
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A Correct answer
Explanation

For two circles with radii r₁=19cm and r₂=10cm, the distance between centers when the length of the direct common tangent L=12cm is given by d = √(L² + (r₁-r₂)²) = √(144 + 81) = √225 = 15cm. This formula comes from the right triangle formed by the line connecting centers, the radius difference, and the common tangent. Option B (20cm) would require a different tangent length, and Options C and D don't satisfy the geometric relationship.

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