(1) FI is parallel to the bisector AH of angle A.

(2) The line IG, orthogonal to AB at the "cleaver point" I, passes through the middle G of the arc BAC of the circumcircle of triangle t.

(3) The three cleaver-lines, corresponding to the middles of the three different sides intersect at a point K.

(4) K is the incenter of the medial triangle s, whose vertices are the middles of the sides of t.

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