Analytic geometry
02-18-2019, 03:16 PM
Post: #3
 Albert Chan Senior Member Posts: 2,701 Joined: Jul 2018
RE: Analytic geometry
(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
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 Messages In This Thread Analytic geometry - yangyongkang - 02-18-2019, 09:27 AM RE: Analytic geometry - yangyongkang - 02-18-2019, 12:09 PM RE: Analytic geometry - Albert Chan - 02-18-2019, 08:48 PM RE: Analytic geometry - Albert Chan - 02-18-2019 03:16 PM RE: Analytic geometry - Albert Chan - 02-18-2019, 05:51 PM RE: Analytic geometry - Albert Chan - 02-19-2019, 10:23 PM RE: Analytic geometry - Albert Chan - 02-20-2019, 09:33 PM

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