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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

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

I found only one:8/5. What did I do wrong?

IneedHALP  Mar 3, 2019

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

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