Are there nine?

Geometry Level 4

A \(\triangle \space ABC\) with its sides \(AB, BC \space and \space CA\) having a slope of

  • \({m}_{BA}=\tan 15^\circ\)
  • \({m}_{BC}=\tan 75^\circ \)
  • \({m}_{CA}=\tan 135^\circ \)

While constructing the nine point circle , how many points will the circle have in common with the triangle.?

Clarification: Having a point in common means that the circumference of the circle and the three sides of the triangle are intersecting (and/or) touching each other.

This question is part of the set Geometry problems.

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