In this video, I'm going to examine circles and lines that are tangent to the circles. So for example, let's say I want to draw a line from point B over here to the circle, and I want that line to be attached to the circle at just one point of tangency. What you don't want to do is try to eyeball it and get it kind of close. It'll be a chord, or it'll miss the circle. You'll never get it exact. What you need to know is how this is constructed geometrically.

The solution is to find the midpoint between points A and B. I'll use this tool right here that puts in the midpoint. And then I will label that as point C. I can then draw a circle from C to A. And then I'll also label these two points where the circles cross. Those are the points of tangency. So all I have to do is draw in a line from B to D and from B to E And those lines are precisely tangent to the circle at those points. We can do this a little bit more easily.

And I'll just show you that down below, I'm going to make a parallel line here, which I will call the red. And also drawn a circle over here, which is the circle I'm trying to get something tangent to. And I'll make that blue. Also label that as point f. and put a point over here somewhere along the line and a label that point G. So if I want to draw a tangent line now, I can use this specialized tool right here. And the way that it works is you can tap on the point first, and then the circle and it will put in the line or you can tap on the circle first, and then the point, either way is fine. And it will draw those lines in tangent to the circle.

Optionally If you want you can find the points of intersection with this tool. And those the points of tangency right there which I will label as H and I