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Math Help - 9 Point circle of 3-4-5 right triangle

  1. #1
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    Question 9 Point circle of 3-4-5 right triangle

    This was a question in the urgent help section, but I figured out what I needed, so if a mod could delete that thread, or lock it, that would be appreciated.

    I'm just trying to understand something on a problem. It states that a 3-4-5 right triangle has 5 distinct points defining it's 9 point circle. However, whenever I try to draw this out, I only get 4 points.

    Someone else emailed the professor about this (The professor wrote 8 instead of 5), but that person found 5 points, and the professor said it should be 5 points. Any insight into what I may be doing wrong?

    These are the points I got.
    1)Midpoint (c), Euler (b) are the same
    2)Altitude (b), Altitude (c), Euler (a), A, H, are all the same
    3)Midpoint (b), Midpoint (c) are the same
    4) Midpoint (a), Altitude (a), O, are all the same.
    Thanks!
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  2. #2
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    Sorry, your Web browser is not Java compatible. This prototype will not be of much interest to you.
    Quote Originally Posted by monsieur fatso View Post
    This was a question in the urgent help section, but I figured out what I needed, so if a mod could delete that thread, or lock it, that would be appreciated.

    I'm just trying to understand something on a problem. It states that a 3-4-5 right triangle has 5 distinct points defining it's 9 point circle. However, whenever I try to draw this out, I only get 4 points.

    Someone else emailed the professor about this (The professor wrote 8 instead of 5), but that person found 5 points, and the professor said it should be 5 points. Any insight into what I may be doing wrong?

    These are the points I got.
    1)Midpoint (c), Euler (b) are the same
    2)Altitude (b), Altitude (c), Euler (a), A, H, are all the same
    3)Midpoint (b), Midpoint (c) are the same
    4) Midpoint (a), Altitude (a), O, are all the same.
    Thanks!
    I see five points of intersection...
    note that this is a 3-4-5 triangle, although you can move the red points to see where you went wrong
    Also, green lines are altitudes
    Last edited by Quick; November 23rd 2006 at 06:51 PM. Reason: Editing drawing
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  3. #3
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    ahhh. Blast. Yeah, I was putting the altitude out of the right angle to be the same as the median, which I shouldn't have just assumed was correct. Thanks a ton!
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  4. #4
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by monsieur fatso View Post
    ahhh. Blast. Yeah, I was putting the altitude out of the right angle to be the same as the median, which I shouldn't have just assumed was correct. Thanks a ton!
    you're welcome
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