Math Is Fun Forum

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...

Thomas11

Guest

Re: 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 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...

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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igloo myrtilles fourmis

Thomass

Guest

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.

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

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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Numbers are the essence of the Universe

Thomas11

Guest

Re: Geometric proof wanted (triangle, bisector)

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?

Thomas11

Guest

Re: Geometric proof wanted (triangle, bisector)

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.

Thomas11

Member

Registered: 2007-02-01

Posts: 15

Re: Geometric proof wanted (triangle, bisector)

Here's a picture of the problem

Thomas11

Member

Registered: 2007-02-01

Posts: 15

Re: Geometric proof wanted (triangle, bisector)

Did the picture help you to understand my problem?

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

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Numbers are the essence of the Universe

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

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Numbers are the essence of the Universe

Thomas11

Member

Registered: 2007-02-01

Posts: 15

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

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.

Thomas11

Member

Registered: 2007-02-01

Posts: 15

Re: Geometric proof wanted (triangle, bisector)

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)

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 -.-')

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.

Thomas11

Member

Registered: 2007-02-01

Posts: 15

Re: Geometric proof wanted (triangle, bisector)

Help me...-.-