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Comparing Line Segments in Two Circles

Two circles, with radii a and b, are tangent to each other and to line AB, as shown. Compare the lengths of segments AB and OP. Interpret your result.

Compare the lengths of segments AB and OP. Interpret your result.

 

 

Hints

One solution.

Comments:

Look for the relationship to the Arithmetic Mean-Geometric Mean of two positive values to this configuration. Note that the length of QP is a + b.

Reference: See the cover of the June 1985 issue of the College Mathematics Journal .