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RE: Triangle Proof II
Posted:
Jun 30, 2004 4:59 AM
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> -----Original Message-----
> From: owner-geometry-puzzles@mathforum.org [mailto://owner-geometry-
> puzzles@mathforum.org] On Behalf Of Eamon
> Sent: Wednesday, June 30, 2004 7:08 AM
> To: geometry-puzzles@mathforum.org
> Subject: Triangle Proof II
>
> ABC is an ARBITRARY triangle.
> D lies on BC and E lies on AC.
> Prove that if AD = BE then the triangle is isosceles.
>
>
>
>
> y| C
> | /\
> | / \
> | / \ D
> | E/ \
> | / \
> | / \
> ____|/__________________\B____
> A| x
The result is of course false. More conditions should be added.
Example: Take a non-isosceles triangle ABC.
From A draw a circle of arbitrary radius cutting BC at D (plus another
point). With the same radius draw a circle with B as centre,
cutting AC at E (plus another point). That does it.
Note, there is an abundance of such radii. All you need is to pick a
length greater than the largest of the altidudes of the triangle.
Regards.
Michael Lambrou
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