# 9 Point circle of 3-4-5 right triangle

• Nov 16th 2006, 04:33 PM
monsieur fatso
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!
• Nov 16th 2006, 05:14 PM
Quick
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Quote:

Originally Posted by monsieur fatso
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
• Nov 16th 2006, 06:04 PM
monsieur fatso
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!
• Nov 16th 2006, 06:11 PM
Quick
Quote:

Originally Posted by monsieur fatso
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 :)