Re: [Math4u] Please answer this question

http://www.mathopenref.com/isosceles.html

Isosceles triangle: A triangle which has two of its sides equal in length.

http://www.thefreedictionary.com/triangle

Isosceles triangle - a triangle with two equal sides

 

http://www.thefreedictionary.com/triangle

Equiangular triangle, equilateral triangle - a three-sided regular polygon

 

http://en.wikipedia.org/wiki/Isosceles_triangle

In an equilateral triangle, all sides are of equal length. An equilateral triangle is also an equiangular polygon, i.e. all its internal angles are equal—namely, 60°; it is a regular polygon[1] In an isosceles triangle, two sides are of equal length. An isosceles triangle also has two congruent angles (namely, the angles opposite the congruent sides). An equilateral triangle is an isosceles triangle, but not all isosceles triangles are equilateral triangles.[2]

 

E=set of all triangles. Represent this by the circle

X^2 + y^2 = 100

A=set of all isosceles triangles. Represent this by the circle

X^2 + (y-5)^2 = 25

B=set of all equilateral triangles. Represent this by the circle

X^2 + (y-7.5)^2 = 6.25

C=set of all obtuse triangles. Represent this by the circle

(x-5)^2 + y^2 = 25

Check:

A, B, and C are inside E.

B is inside A

A and C overlap

B and C must not overlap.

Distance between (0,7.5) and (5,0) is

Sqrt(5^2 + 7.5^2)

=sqrt((10/2)^2 + (15/2))

= sqrt(325/4)

Sum of radii = 2.5 + 5 = 7.5=15/2=sqrt(225/4)

sqrt(325/4) > sqrt(225/4) ok, the circles do not intersect.

Regards,

Brian

----- Original Message -----

From: Rob van Wijk

To: Math4u@yahoogroups.com

Sent: Saturday, October 27, 2007 2:34 PM

Subject: Re: [Math4u] Please answer this question

Comments inside

-------- Original-Nachricht --------
> Datum: Fri, 26 Oct 2007 01:55:00 +0200
> Von: "Douglas Anderson" <djandersonza@gmail.com>
> An: Math4u@yahoogroups.com
> Betreff: Re: [Math4u] Please answer this question

> So what, would it be three circles (A,B,C) contained in a large circle E?
> I have to admit being an absolute tyro when it comes to Venn Diagrams as
> this request was the first time I have heard of them, yet the request
> piqued my interest.
> So as a tyro maybe I can help ch_mshahid with the help that Rob has
> offered.
> My error cam in because I misunderstood the wording. Actually, I read the
> query too quickly and thought he wanted one diagram to represent all
> possibilities.
> The three triangles, Isoceles can, in a special case, be considered
> equilateral. This would be the case when the base of teh triable is equal
> in length to the two sides. Hence every equilateral triangle is
> potentially isoceles.
> (Rob, would this be a correct assumption)

Actually, I have no idea what an isosceles triangle is (English is not my
native language); I'm perfectly sure I'd know if you told me the Dutch word
for it, but I'm very much pressed for time, so can't look it up, sorry.

> Now in the case of obtuse or scalene triangles. These to can be isoceles
> if two of the sides are of equal length. However, no scalene (obtuse)
> triangle could ever be equilateral.
> So as far as I can figure it, the cirlce representing equilateral
> triangles would be be wholly enclosed within the circle representing
> Isoceles triangles.
> Scalene can in special circumstances be Isoceles. Hence there would be an
> overlap between these two groups. However, since no equilateral triangle
> can be isoceles, there would be no overlap between these two, so
> (I have tried to include a sketch but cannot seem to have it included)
> B would be wholly indluded within A, and there would be an overlap
> between C and A but not C and B.
> Hope my words can portray what would have been better as a picture

Here's the picture (copy-paste to notepad or wordpad or whatever and choose
"Courier New" as font if it looks weird:

+--------------------+
| |
| +----------+ E |
| | | |
| | A +--+-----+ |
| | +---+ | | | |
| | | B | | | C | |
| | +---+ | | | |
| | +--+-----+ |
| | | |
| +----------+ |
| |
+--------------------+

(The original question also included a set E for Everything (all
triangles), which was missing from your post.)

HTH,
Rob

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