Multiple choice

The radii of two circles are 4.5 cm and 3.5 cm, respectively. The distance between the centres of the circles is 10 cm. What is the length of the transverse common tangent?

  1. 4 cm

  2. 5 cm

  3. 6 cm

  4. 10 cm
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C Correct answer
Explanation

The length of the transverse common tangent is given by the formula sqrt(d^2 - (r1 + r2)^2), where d is the distance between centers and r1, r2 are the radii. Here, d = 10, r1 = 4.5, and r2 = 3.5, so r1 + r2 = 8. The calculation is sqrt(10^2 - 8^2) = sqrt(100 - 64) = sqrt(36) = 6 cm.

AI explanation

The length of a transverse common tangent between two circles is given by the formula square root of (d^2 - (R1 + R2)^2), where d is the distance between centres. Substituting the given values gives the length as the square root of (10^2 - (4.5 + 3.5)^2). This simplifies to the square root of (100 - 8^2), which is the square root of (100 - 64). The length of the transverse common tangent is 6 cm.

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