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# Circle O and circle P, with radii 3 and 5, respectively, are both tangent to line L at H. Enter all possible lengths of line OP

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

Mar 3, 2019

#1
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Have you tried drawing it?

It seems to me that both circles are on the same side of the line or

They are on opposite sides of the line.

SO I think there is only 2 possible lengths of OP.  You can sketch the diagram and find these 2 lengths all by yourself.

You can let me/us know how you get on or you can ask questions if you like. :)

Mar 3, 2019
#2
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I found only one:8/5. What did I do wrong?

IneedHALP  Mar 3, 2019
#3
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Hi   IneedHALP,

Thanks for interacting with me :)

There is one when they are both on the SAME side of the tangent.

and there is one when the are on OPPOSITE sides of the tangent.

draw IT !  AND you will see.

Do you know what all the words mean?  Like tangent and radius?

1)  Draw the tangent first. (That is just a line)

2)  Now put the point H on it.

You need two pics. When when the circles are both on the same side.

and on opposite sides

draw it and work out haw far apart the centres are.

Note: a tangen is a line that only just touches the circle. It only makes contact in one place.

Mar 3, 2019