tangent to a circle: How do I draw this from the textual description?

[jaideepdesai]

Two different points P and Q are given on one side of line AB. Draw a circle passing through the points P and Q touching the line AB in point R. How do I draw this?

 

[tkhunny]

Two different points P and Q are given on one side of line AB. Draw a circle passing through the points P and Q touching the line AB in point R. How do I draw this?

Any way you can and in such a way that all the requirements are met.

 

[Dr.Peterson]

Two different points P and Q are given on one side of line AB. Draw a circle passing through the points P and Q touching the line AB in point R. How do I draw this?

Are there other conditions, such as a compass-and-straightedge construction, or can you use coordinates or something?

Is point R given, or not?

 

[Dr.Peterson]

If R is not given, and you do want a compass-and-straightedge construction, one way to start would be to draw line PQ and think about a theorem that involves a secant line PQ and a tangent line intersecting at a point.

It may also be worth noting that there will typically be two such circles (with different R).