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Math Help - locus of orthocentre

  1. #1
    Senior Member abhishekkgp's Avatar
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    locus of orthocentre

    ABC is an acute angled triangle. P is a point on BC. X and Y lie on AB and AC respectively such that XP is perpendicular to AB and YP is perpendicular to AC. what is the locus of the orthocentre of the triangle AXY as P moves on BC?
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    Quote Originally Posted by abhishekkgp View Post
    ABC is an acute angled triangle. P is a point on BC. X and Y lie on AB and AC respectively such that XP is perpendicular to AB and YP is perpendicular to AC. what is the locus of the orthocentre of the triangle AXY as P moves on BC?
    As a starter so that you know what you should get ...
    Attached Thumbnails Attached Thumbnails locus of orthocentre-loc_orthocent.png  
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  3. #3
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by earboth View Post
    As a starter so that you know what you should get ...
    thats right but how do i proceed from here?
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    If you observe the image you can see that x, P,y and the orthocenter form a parallelogram. As P changes its position, the shape of the parallogram changes. When P is at B and C, it becomes a straight line. So the red line in the image is the locus of the orthocenter.
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  5. #5
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by sa-ri-ga-ma View Post
    If you observe the image you can see that x, P,y and the orthocenter form a parallelogram. As P changes its position, the shape of the parallogram changes. When P is at B and C, it becomes a straight line. So the red line in the image is the locus of the orthocenter.
    so is the locus a STRAIGHT line?
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    Yes.
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