Re: Geometry with circle and three points.
- From: "mina_world" <mina_world@xxxxxxxxxxx>
- Date: Sat, 25 Aug 2007 16:25:08 +0900
"mina_world" <mina_world@xxxxxxxxxxx> wrote in message
news:fan4uj$5v4$1@xxxxxxxxxxxxxxxxxxx
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.
I want to show the Uniqueness.
But I don't know well.
So, I need your advice.
I think....
1) The perpendicular bisector of a chord goes through the centre of the
circle.
2) There is a unique point that intersect with the perpendicular bisectors
of the sides.
3) The center of circle is equidistant from three points.
I know that
The perpendicular bisector of a chord goes through
the centre of the circle.
For 3 points A, B, C,
Construct the perpendicular bisector of segment AB.
Construct the perpendicular bisector of segment BC.
We can find a unique point of intersection.
It means that this point of intersection is a center of circle.
In fact, this point of intersection is circumcenter.
Of course, I know that
There is a unique point that intersect with the perpendicular bisectors of
the sides.
so, there is a unique center of circle about given three points.
and
The center of circle is equidistant from three points.
It means that this unique circle is circumscribed circle.
.
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