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#1 2007-09-22 18:28:46

th-moon
Guest

Unsolved problem

We have an angle (less than 180 degree) with it's top in point P. We also have point A inside the angle (interior). Points X and Y are laying on different legs of this angle and |PX| = |PY|.

We must prove that when the sum: |AX| + |AY| is the smallest (minimum), the equation belove is correct:

Angle XAP is equal to angle YAP.


P.S Point A is "standing still", and can be anywhere inside the triangle. We only move X and Y points.

#2 2007-09-23 01:32:30

landof+
Member
Registered: 2007-03-24
Posts: 131

Re: Unsolved problem

Is point p the vertex of the angle?

Anyway, I don't fully get it, but to my understanding so far, then AX and AY must be equal in length right....?


I shall be on leave until I say so...

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#3 2007-09-23 01:54:45

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Unsolved problem

I am assuming that PX, PY, and the angle XPY are fixed but X and Y are free to move about (subject to |PX| = |PY|). Then the sum of |AX| and |AY| is minimum when |AX| = |AY|. When this happens, triangles PAX and PAY are congruent (SSS property), and so PÂX and PÂY are equal.

Last edited by JaneFairfax (2007-09-23 01:56:34)

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#4 2007-09-23 03:49:45

th-moon
Guest

Re: Unsolved problem

landof+, yes: point P is the vertex of the angle. (sorry for my english)

I hope this will be helpful:
First we choose point A (inside angle). We consider every pair of points X,Y which are on the legs of this angle and implement condition: PX=PY. We should find this points X,Y for which value of sum AX+AY will be smallest.

At the end we should prove that:
angle XAP is equal to angle YAP

#5 2007-09-26 05:14:16

th-moon
Guest

Re: Unsolved problem

Can anybody help me?

#6 2007-09-26 06:29:38

th-moon
Guest

Re: Unsolved problem

Could you explain why: "the sum of |AX| and |AY| is minimum when |AX| = |AY|." ?

#7 2007-10-05 09:32:50

th-moon
Guest

Re: Unsolved problem

please, help - i still have no idea how to solve this problem

#8 2007-10-05 22:39:03

Monser
Guest

Re: Unsolved problem

Please contact me: email address removed, so I can give you some tips.

If you wish for help, simply visit the forum.  We will post responses here for all to see.  There is no need for posting your email address. - Ricky

#9 2007-10-06 02:35:18

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: Unsolved problem

While we are very appreciative of you offering to help people, we'd rather not have you give out your email like that, just to prevent people/bots spamming you. wink

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