More explanation of Tutorial 3, Question 5
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In the diagram above, you can click and drag to move the points A, B, and C. The point D is the midpoint of BC, and the point E is the intersection of the perpendicular bisector of BC with the angle bisector of angle BAC.
The line EF is perpendicular to AB and the line EG is perpendicular to AC. You can see now that the point E is outside the triangle (see the Tutorial 3 solutions for a general proof). Moreover, one of the points F or G is outside the triangle, while the other point is inside the triangle, thus making the last step of the proof invalid (again, see the solutions for more details).
