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# help geometry

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Circle O and circle P, with radii 3 and 8, respectively, are both tangent to line l at H. Enter all possible lengths of OP separated by commas.

Aug 18, 2021

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Because both circles are tangent to the same spot, the centers of the circles and the point of tangency form a line. There are two distances: one where both circles are on the same side, or where the circles are on seperate sides.

If the two circles are on the same side, the distance would be 8 - 3 = \$\boxed5\$

If the two circles are on different sides, the distance would be 8 + 3 = \$\boxed{11}\$

Aug 18, 2021