Thread: Prove that there is a unique circle...

Let A be a point on a line l, and let B be a point that does not lie on l. Prove that there is a unique circle that contains A and B and is tangent to l.

This is obviously true, but I am getting nowhere. Can I have any help please?

Originally Posted by TimsBobby2

Let A be a point on a line l, and let B be a point that does not lie on l. Prove that there is a unique circle that contains A and B and is tangent to l.

There a unique ray that is perpendicular to that is in the

Let be the perpendicular bisector of .

Can show that

Is that point the center of the circle?

What do you mean the B side unioned with l? That's more confusing to me really, could you be a little more clear?

Originally Posted by TimsBobby2

What do you mean the B side unioned with l? That's more confusing to me really, could you be a little more clear?

I assumed you were in an axiomatic geometry course.
But I guess you are not.

There is a unique plane, , determined by

Look at the unique perpendicular to at that is in .

That perpendicular will intersect the perpendicular bisector of .

That is the center of your circle.