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*Incircle, Excircles, and the 9-Point Circle

Facts:
  • point I is the center of your triangle's incircle.
  • point N is the center of the 9-point circle
  • points H, M, & L are circle N's points of tangency with the excircles.
  • point O is where circle N and circle I are tangent to each other.

There are four circles tangent to three sides of a triangle...

And one circle tangent to all four circles.

9-Point Circle

What do you think the 9 points of the 9 point circle are?

Can you construct a 9-Point Circle Below? (worth 5 points on any former assessment; capped at 92%).