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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.
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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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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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
Can anybody help me?
Could you explain why: "the sum of |AX| and |AY| is minimum when |AX| = |AY|." ?
please, help - i still have no idea how to solve this problem
Please contact me: email address removed, so I can give you some tips.
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