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#1 2007-02-01 01:10:08

Thomas11
Guest

Geometric proof wanted (triangle, bisector)

Hello, that is my problem:
There is a triangle ABC. On the side AC there is a point D and on the side BC there is a point E. Besides you must notice that the line segment AD is as long as the line segment BE. So: AD=BE
Then one examines the circumscribed circles of the two triangles, which are a part of the triangle ABC, AEC and BDC. These circumscribed triangles subtend each other at the point C and at another point F. Finally it is to prove that the line segment with the starting point C and the ending point F is the bisector of the angle gamma (the angle at the point C).

    Please help me, I am nearly desperate... I just don't know how tpó proof this...

#2 2007-02-01 01:20:16

Thomas11
Guest

Re: Geometric proof wanted (triangle, bisector)

Thomas11 wrote:

Hello, that is my problem:
There is a triangle ABC. On the side AC there is a point D and on the side BC there is a point E. Besides you must notice that the line segment AD is as long as the line segment BE. So: AD=BE
Then one examines the circumscribed circles of the two triangles AEC and BDC, which are a part of the triangle ABC. These two circumscribed triangles subtend each other at the point C and at another point F. Finally it is to prove that the line segment with the starting point C and the ending point F is the bisector of the angle gamma (the angle at the point C).

    Please help me, I am nearly desperate... I just don't know how tpó proof this...

#3 2007-02-01 01:30:49

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Geometric proof wanted (triangle, bisector)

This is hard for me.  I drew 3 scenarios, with odd lengths, and sure enough the sketches do tend to agree with the bisection of angle, but I have no idea how to prove this, sorry.

Last edited by John E. Franklin (2007-02-01 01:31:30)


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#4 2007-02-01 01:39:35

Thomass
Guest

Re: Geometric proof wanted (triangle, bisector)

John E. Franklin wrote:

This is hard for me.  I drew 3 scenarios, with odd lengths, and sure enough the sketches do tend to agree with the bisection of angle, but I have no idea how to prove this, sorry.

Yeah, I've also alraedy drawn many scenarios, however, I was not able to prove it. darn, that difficult...

#5 2007-02-01 09:21:03

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: Geometric proof wanted (triangle, bisector)

Can anyone draw a picture of it , I am confused since my English is poor


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#6 2007-02-01 09:40:56

Thomas11
Guest

Re: Geometric proof wanted (triangle, bisector)

Stanley_Marsh wrote:

Can anyone draw a picture of it , I am confused since my English is poor

I can.
What's your language?
Could I send it to you via e-mail?

#7 2007-02-01 12:41:37

Thomas11
Guest

Re: Geometric proof wanted (triangle, bisector)

kylekatarn wrote:
Thomas11 wrote:
Stanley_Marsh wrote:

Can anyone draw a picture of it , I am confused since my English is poor

I can.
What's your language?
Could I send it to you via e-mail?

could you please forward a copy to


it would be very helpfull,

thanks; )

I've just sent you an e-mail.

#8 2007-02-01 22:44:20

Thomas11
Member
Registered: 2007-02-01
Posts: 15

Re: Geometric proof wanted (triangle, bisector)

Here's a picture of the problem

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#9 2007-02-02 07:26:02

Thomas11
Member
Registered: 2007-02-01
Posts: 15

Re: Geometric proof wanted (triangle, bisector)

Did the picture help you to understand my problem?

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#10 2007-02-02 08:23:34

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: Geometric proof wanted (triangle, bisector)

Yeah , I am working on that now,don't know if I can solve it though


Numbers are the essence of the Universe

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#11 2007-02-02 08:32:29

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: Geometric proof wanted (triangle, bisector)

What? how can the segment CF besect any angle? Name the angle gamma ,I don't really understand ,lol


Numbers are the essence of the Universe

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#12 2007-02-02 13:07:28

Thomas11
Member
Registered: 2007-02-01
Posts: 15

Re: Geometric proof wanted (triangle, bisector)

kylekatarn wrote:
Stanley_Marsh wrote:

What? how can the segment CF besect any angle? Name the angle gamma ,I don't really understand ,lol

Segment CF bissects angle gamma.

It's segment CD. Segment CF is a part of the triangle side a. Have a look at the picture. wave

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#13 2007-02-02 23:03:20

Thomas11
Member
Registered: 2007-02-01
Posts: 15

Re: Geometric proof wanted (triangle, bisector)

Thomas11 wrote:

Hello, that is my problem:
There is a triangle ABC. On the side AC there is a point E and on the side BC there is a point F. Besides you must notice that the line segment AE is as long as the line segment BF. So: AE=BF
Then one examines the circumscribed circles of the two triangles, which are a part of the triangle ABC, AFC and BEC. These circumscribed triangles subtend each other at the point C and at another point D. Finally it is to prove that the line segment with the starting point C and the ending point D is the bisector of the angle gamma (the angle at the point C).

    Please help me, I am nearly desperate... I just don't know how tpó proof this...

Now the picture matches the exercise, I named s.th. wrong. Now it should be right.

Last edited by Thomas11 (2007-02-02 23:04:10)

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#14 2007-02-06 03:31:07

Thomas11
Member
Registered: 2007-02-01
Posts: 15

Re: Geometric proof wanted (triangle, bisector)

Has anybody found s.th. interesting or helpful yet? (me not -.-')

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#15 2007-02-10 05:22:09

Thomas11
Member
Registered: 2007-02-01
Posts: 15

Re: Geometric proof wanted (triangle, bisector)

Uh, please inform me, even if you only find s.th. that might be helpful, I'll appreciate your efforts.

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#16 2007-02-15 03:17:23

Thomas11
Member
Registered: 2007-02-01
Posts: 15

Re: Geometric proof wanted (triangle, bisector)

Help me...-.-

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