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Math Help - locus question. perpeendiculars dropped to three sides.

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    Senior Member abhishekkgp's Avatar
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    locus question. perpeendiculars dropped to three sides.

    Find the locus of the points P within a given triangle ABC such that the distances from P to the sides of the given triangle can themselves be the sides of a certain triangle.
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    Re: locus question. perpeendiculars dropped to three sides.

    Quote Originally Posted by abhishekkgp View Post
    Find the locus of the points P within a given triangle ABC such that the distances from P to the sides of the given triangle can themselves be the sides of a certain triangle.
    Let A',\, B',\, C' be the points where the angle bisectors at A,\,B,\,C meet the opposite sides of the triangle. My guess is that the condition for P is that it must lie inside the triangle A'B'C'. I think (without having checked carefully) that I can prove this using coordinate geometry, but I don't see how to tackle it using euclidean methods.
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