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.

Guest Aug 18, 2021

#1**0 **

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 = $\boxed{11}$

SparklingWater2 Aug 18, 2021