Morley's trisector Theorem

In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle.

1. what will happen if try to move the points or the side of the triangle ABC? 2. What's a reasonable explanation for this? 3. Do you think the trisector theorem relates to circumcenter theorem?