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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
avatar+99324 
+1

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. :)

 

 

PLEASE NO ONE ANSWER OVER ME.

 Mar 3, 2019
 #2
avatar+80 
+1

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

IneedHALP  Mar 3, 2019
 #3
avatar+99324 
+1

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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