Thanks, this is interesting. Also I just noticed an error in my second diagram when I renamed my variables: Θty should beΘtx everywhere except in the cutout triangle, where it's correctly labeled. I'm pretty sure the calculations themselves are still correct. I'll update the image.
Never mind...
I can't tell if this is just a coincidence of the values I chose, but the distance from the x-axis to the circle's center (Dy) worked out to be equal to the distance from the origin to the tangent line's intersection (T). Weird.
This question occurred to me a few days ago and it's been bugging me ever since.
Consider a circle in the coordinate plane with center P(x,y) and radius R, where R < D, D being the distance from the origin to the circle's center.
There are two lines tangent to the circle (T1 and T2) that pass...