Analytic geometry

[Albert Chan]

(02-18-2019 09:27 AM)yangyongkang Wrote:  Hello everyone. I recently encountered a planar geometry problem, I tried to solve it with algebraic methods.
This requires me to solve a series of equations ...

There is no need to solve this: see http://www.hpmuseum.org/forum/thread-123...#pid111897

Any line in the form x cos(m) + y sin(m) = 1 had distance of 1 to the origin.
in other words, all these lines are tangent to the unit circle.

Quote:Its geometric meaning is an equilateral triangle surrounded by three tangents of a circle.

I think you meant a triangle (not necessarily equilateral), tangents of a unit circle.
But, if you really want a equilateral triangle, it is trivial:

line 1: whatever angle m you pick
line 2 and line 3: use angle m ± 2Pi/3