1. Introduction: How Many Tangents Can You Draw?
You already know what a tangent is. A tangent is a straight line that touches a circle at exactly one point. That single touching point has a name: the point of contact.
Now let me ask you a different question. Not "what is a tangent" — but "how many tangents can you draw from a given point?"
Pick up a coin. Imagine a fly sitting somewhere near it. From where the fly sits, how many straight lines can it draw that just touch the rim of the coin without cutting through it?
Stop scrolling. Try it in your head before reading on.
The answer depends on where the fly is sitting. That is the whole game today. Where the point sits decides everything.
Let me show you three places the fly could sit.