TWo circles of radii 5 cm and 3 cm touch externally, then the ratio in which the direct common tangent to the circles divides externally the line Joining the centers of the circles is:

Let the two circles have centers $O_1$ and $O_2$ with radii 5 cm and 3 cm, respectively.

The distance between their centers is:

$ O_1O_2 = 5 + 3 = 8 \text{ cm} $

Let $T$ be the external point where the direct common tangent meets the line joining the centers externally in the ratio $k:1$. The ratio is given by:

$ \frac{O_1T}{O_2T} = \frac{r_1}{r_2} = \frac{5}{3} $

Thus, the ratio in which the direct common tangent divides the line joining the centers externally is:

$ \boxed{5:3} $

Here is the solution :

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