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20 1 1 the solution of the thirteenth question in the mathematics test of Henan senior high school entrance examination.
According to the shortest vertical line segment, when DP⊥BC, the length of DP is the smallest.

∵BD⊥CD, that is, ∠ BDC = 90, and ∠ A = 90,

∴∠A=∠BDC, and ∠ADB=∠C,

∴∠ABD=∠CBD, and DA⊥BA, DP⊥BC,

∴AD=DP，AD=4，

∴DP=4.

So the answer is: 4.

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