# 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.

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