Equation of Circle Given 2 Tangent Lines and a Point

Geometric set up 1:15 Steps required given at 5:36 and Example starts at 9:25

[StripeyType]

I'm so pleased to have found this video, and the reason may be surprising. During isolation, I've taken to trying for the first time to make a knife, something I've always wanted to do; I am using an old piece of leaf spring. the piece is fairly-well rectangular, except that the ends are trapezoidal. I want to find a graceful and beautiful curve (two, in fact - the design is what's called a 'drop point' which is typically two intersecting circular arcs to form the point) the circles are not typically of the same radius, but I must construct them given the line segments formed by the edges of the piece of steel I'm working with. As I was falling asleep last night I realized that I could do this by constructing circles precisely as you've done here!
So yeah, finding the line which bisects the angles between my segments, and now I know the line(s) along which the center(s) must lie, and I even can bound the radius given the dimensions of my steel's features again... and really since I don't need mathematic precision for a piece of steel with rust pits measured in large fractions of millimeters, I can iteratively approximate with a compass until... voila!

All of which is a long-winded way of saying "Thank you"

[tkhagos]

This is how a math should be thought...Mr. Tarrou's Chalk Talk videos are well organized and step by step...he explains it like for a six years old even the advanced ones like in this video...fan to watch

[TURKISTONIM]

I didn't understand half of the video thanks to you

[profrobbob]

#math   #trigonometry   #analyticalgeometry  

[WelshGuitarDude]

How would you find the biarc that connects a start point and a start direction (which is magnitude 1 and tangent at start point) to the end point with its end direction (which is magnitude 1 and tangent at the end point). The math for it is hard, I couldn't work out how to find the two arcs.

[killgoogle]

Is there another method to do this? Or do you have to use the angle bisector?

[theofficialdoc_]

Can I just say, No chalks were harmed in the making of this video. 😁