But we also need to go fight each other.

但我们还需要互相切磋较量。

Pro tip, anytime you're doing geometry with circles or spheres, keep at the forefront of your mind that anything tangent to the circle is perpendicular to the radius drawn to that point of tangency.

提示， 任何时候你在处理与圆或有关的几何问题时，都要记住， 任何与圆相切的直线都垂直于连接该切点的半径。

I am now going to move it up to the next check point and you can see I am trying to move my pencil so that it is tangent to that line.

我现在要把它移动到下一个检查点，你可以到我正在尝试移动我的铅笔，使其与那条线相切。

Near the magnetic poles of a neutron star, an electron can be accelerated by the magnetic field and emit a so-called curvature photon, tangential to the magnetic field line.

在中星磁附近，电可以被磁场加速并发射与磁场线相切的所谓曲率。

The two long axes of this rectangle are completely tangential to the circle, so they are part of the architectural design of Stonehenge.

这个矩形的两条长轴完全与圆相切，因此它们是巨石阵建筑设计的一部分。

This line is tangent to the circle.

这个直线和圆相切。

Finally, you draw a curve that's tangent to each wavelet, meaning that it touches each half circle at exactly one point.

最后，绘制一条与每个小波相切的曲线，这意味着它恰好在一个点接触每个半圆。

And then similarly, if you draw the line on the tangency point of the sphere for the red and the green, it's one of those external tangents that goes to the other one, and likewise over here.

然后类似地， 如果你在红和绿相切点处画一条线，这条线就是那些外切线之一， 它会延伸到另一个上，这里也是一样。

Radius must be smooth and blend into the face.

圆弧必须滑且与平面相切。

We start off by drawing the square whose side lengths  are all tangent to that circle.

我们首先画一个正方形，其各边都与该圆相切。

And again, since this is a point where the corner sphere is tangent to the inner sphere, it's also a point of the inner sphere.

而且，由于这一点是角落与内相切的地方，它也是内上的一个点。