Thread: finding the smallest perimeter or a triangle

Hi,

This is my question and I'm not even sure how to start it...feels like there are so many possibilities...

Given an angle defined by rays r1 and r2 (you may assume it is an acute angle) and a point P interior to this angle find points X on r1 and Y on r1 such that the triangle PXY has the smallest perimeter. Provide proof that the points are indeed optimal.

Thanks!!!

In the figure PX & PY are perpendicular to the two rays of the angle.
It is claimed that has least perimeter.
We know that PX’ is longer that PX for any X’ on that ray other that X.
Can you finish?

Not very clear.

and a point P interior to this angle find points X on r1 and Y on r1 such that the triangle PXY has the smallest perimeter

Triangle PXY?
Meaning, P is the intersection, or the origin, of rays r1 and r2?
I thought P is supposed to be inside the angle formed by r1 and r2.

hmm it's like the picture drawn above..i think i may have a better idea on how to solve this now..thank you!

Originally Posted by ticbol

Not very clear.

I disagree. It clearly says that P is in the interior of the angle.
But maybe it just seems clear to me because it is such a well know problem in axiomatic geometry courses.

Originally Posted by Plato

I disagree. It clearly says that P is in the interior of the angle.
But maybe it just seems clear to me because it is such a well know problem in axiomatic geometry courses.

It was not very clear to me when I wrote my first reply. I have not seen your diagram then yet, and the asker has not confirmed it yet. Have I known the figure, or has the asker explained it to me even without your diagram, I could have solved the question.

i think the biggest problem I'm having is the wole proof thing...