# 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.