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Eight difficult problems of mathematical geometry in Beijing Normal University
1. The side length of the regular triangle AEF is equal to the side length of the diamond ABCD. If point E and point F are on BC and CD respectively, what is the degree of angle B?

2. As shown in the figure, in the known triangle ABC, AD is the bisector of the angle BAC, DE is perpendicular to AB and E, and DF is perpendicular to AC and F, which proves that AD is the middle vertical line of EF.

3. In trapezoidal ABCD, AB//DC, E is the midpoint of waist AD, AB+DC=BC, which proves that BE is perpendicular to CE.