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20 13 Jilin sanmao mathematics
Solution: Establish a rectangular coordinate system as shown in the figure.

Let P(90cosx, 90sinx)

∴pr= 100-90sinx,pq= 100-90cosx

∴spqcr=( 100-90sinx)( 100-90cosx)

= 10000-9000(sinx+cosx)+8 100 sinx cosx

Let sinx+cosx = t ∈ [1, 2]

∴sinxcosx=t2? 12

∴sPQCR=4050t2-9000t+5950,

When t= 109, the minimum value is 950m2. ..

So the answer is: 950.