Triangle and lines

Geometry Level 3

We have a triangle and a line and three statement about them:

  • The line goes through the midpoint of the incircle of the triangle.
  • The line divides the triangle's area into two equal areas.
  • The line divides the triangle's perimeter into two equal parts.

Is it always true, that if any two of the statement is true, then the third is also holds true?

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