Re: Geometry with circle and three points.
- From: "mina_world" <mina_world@xxxxxxxxxxx>
- Date: Sat, 25 Aug 2007 03:03:42 +0900
"[Mr.] Lynn Kurtz" <kurtz@xxxxxxxxxxxxxxx> wrote in message
news:=x3PRurifhKDSOaWquqMpa5utRo=@xxxxxxxxxx
On Sat, 25 Aug 2007 02:41:47 +0900, "mina_world"
<mina_world@xxxxxxxxxxx> wrote:
Hello sir~
Three points determine a unique circle.
= There is a unique circle that passes through the three points
(Of course, they are not on the same line.)
----------------------------------------------------
Since there is circumscribed circle, Existence is trivial.
You are *assuming* existence when you say "there is a circumscribed
circle". You have to prove that, and the usual way to prove it
determines the center in a unique way. Look at how the circumscribed
circle for a triangle is constructed.
The perpendicular bisectors of the sides of a triangle intersect in a point
that is equidistant from the vertices of the triangle.
But it is not Uniquess.
.
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