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20 1 1 Huairou Yimei Mathematics for Senior High School Entrance Examination 12.
Solution: Draw a circle with D as the center and the length of AD as the radius.

(1) when the circle is tangent to BC, when DE⊥BC,

∫∠ABC = 30,

∴DE= BD,

AB = 6,

∴ad=2;

② When the circle intersects BC, if the intersection point is B or C, then AD= AB=3.

The value range of ∴AD is 2 ≤ AD < 3. Comments: It is the key to solve this problem to distinguish the minimum and maximum ad by using the position relationship between BC and circle.