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Circle O and circle P, with radii 3 and 5, respectively, are both tangent to line \( \ell\) at H. Enter all possible lengths of line OP, separated by commas. 

try to think of every possible configuration and draw them. 

 Feb 18, 2022
 #1
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If they lie on the same side of the line so that the circles are internally tangent, the distance between the centers is 2.

 

If they lie on opposite sides of the line so that the circles are externally tangent, the distance between the centers is 8.

 

Assuming that they both lie in the same plane.

 Feb 18, 2022

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