圆与两条线的交点之间的距离
[英]Distance between intersection of circle and 2 lines
问题描述
I feel like this should be simple, but I am unable to find any solutions.
我觉得这应该很简单，但我找不到任何解决方案。 I am trying to find the distance between the 2 points (red line) where a circle of radius r intersects 2 lines, given the angle between the lines.给定线之间的角度，我试图找到半径为 r 的圆与 2 条线相交的 2 个点（红线）之间的距离。
How can I find the 2 intersecting points?我怎样才能找到2个相交点？
1 个解决方案
解决方案1
0 2021-11-01 17:26:45
It's just a mathematical problem, first you can find the slope of your lines using (respectively for degrees and radians):这只是一个数学问题，首先您可以使用（分别为度和弧度）找到线的斜率：
Then, writing down the equations for the intersections of the lines and (half of) the circle, you obtain:然后，写下直线和（一半）圆的交点的方程，你得到：
Solving the equation imposing to have a unique solution to have the lines as tangents you obtain the intercept:求解具有唯一解的方程，使线作为切线，您将获得截距：
and then:进而：
The y of the lower point is just -y1, so the overall distance is, after some simplifications:较低点的 y 仅为 -y1，因此经过一些简化后，总距离为：
(Degrees)
（度数）
(Radians)
（弧度）
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