Which, if any, of the two molecular geometries is likely to be polar if the outer atoms are identical and there is a difference in electronegativity between the central atom and the outer atoms

Polar molecules are not symmetrical

Explanation:

Even though the structures of the molecules involved were not shown in the question, but I will proceed to give a general explanation of the conditions that describe a polar molecule.

First of all, symmetrical molecules are non-polar and asymmetrical molecules are polar. This is the reason why CF4 will be a nonpolar molecule but H2O will be a polar molecule. Some symmetrical molecules may may posses polar bonds or dipoles but these dipoles eventually cancel out since the molecule is symmetrical in nature.

Summarily, if a molecule possess the same type of atoms attached to the central atom with some symmetry axes, like C3, C4 etc., we will end up with a non polar molecule but if we have a nonplanar molecule, then we will end up finding it to be polar.

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geosphere and hydrosphere.

this is because the geosphere has to do with geological events, while the hydrosphere controls all water on earth.