If a side of Triangle ABC is tangent to its nine- point circle then triangle ABC is isosceles.

How do I prove this?

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- Apr 25th 2009, 10:05 AMshootie300nine point circle proof
If a side of Triangle ABC is tangent to its nine- point circle then triangle ABC is isosceles.

How do I prove this? - May 6th 2009, 07:56 PMfardeen_gen
The nine point circle passes through the midpoints of the sides and the feet of the altitudes, so if it's tangent to a side, the altitude to that side is the perpendicular bisector of that side. I think you can go from there.