Two circles of radii 18 cm and 12 cm touch each other externally. Find the length (in cm) of their direct common tangent.

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Let the radii of the two circles be r1 = 18 cm and r2 = 12 cm. The distance between their centers (since they touch externally) is D = r1 + r2 = 18 + 12 = 30 cm.

The formula for the length of the direct common tangent (L) between two circles of radii r1 and r2, with centers separated by distance D, is:

L = √[D^2 - (r1 - r2)^2]

Substitute the values:
D = 30, r1 - r2 = 18 - 12 = 6

L = √[30^2 - 6^2] = √[900 - 36] = √864

Now, √864 = √(144 × 6) = 12√6

Therefore, the length of the direct common tangent is 12√6 cm.

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