Is there a formula for finding the center point or radius of a circle given that you know two points on the circle and one of the points is perpendicular to the center?
I know that only having two points is not enough for determining the circle, but given that the center is on the same x coordinate as one of the points, is there a way to use those two points to find the center/radius of the circle?
So you have the following data:
x0 = 0
y0 = 0
x1 = 3
y1 = 1
y2 = ?
I want to build some ramps for my rc car and am trying to figure out the optimal curve for the ramps. The two points are the corners of a 3'x1' piece of plywood. I want to cut the best curve out of the plywood for the jump, and would like to have a formula to calculate/draw the curve for other size ramps.
Here is a diagram of the problem I am trying to solve. The rectangle will basically be a piece of plywood and the curve will be cut out of it. I am trying to solve for y2.
Basically, I am going to pin a piece of string in the ground y2 feet away from my board and attach a pencil to one end in order to mark the curve that I need to cut.
Thank you very much for your help.
Best Answer
It would help to convert this to a question about triangles instead. Pictured again below with a few modifications. (I'll use degrees as it is more common for household projects, but can easily be changed into radians as needed)
As the angle pointed to by the yellow arrow is $\arctan(\frac{1}{3})\approx 18.43^\circ$, that means the red angles are $90^\circ - \arctan(\frac{1}{3})\approx 71.57^\circ$
So, we have a $71.57, 71.57, 36.86$ triangle.
By the law of sines, $\frac{A}{\sin(a)}=\frac{B}{\sin(b)}$ you have $B = (\sqrt{3^2+1^2}\frac{\sin(71.57^\circ)}{\sin(36.86^\circ)}) \approx 5.0013$