two nice theorems in plane geometry

There are two very nice theorems I've learned not so far. The theorems were discovered by Frank Morley and John Conway.

1. Morley's trisection theorem
in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle.

2. Conway's circle
if you continue the sides of a triangle beyond every vertex at the distances equaling to the length of the opposite side, the resulting six points lie on a circle, which is called Conway’s circle.