Seek the analysis of the last question of the mathematics fill-in-the-blank problem in Hangzhou senior high school entrance examination in 2009.

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Here's the original problem.

The first empty one

That is, a semicircle inscribed with a square.

Let the center of the circle be O and connect OE.

Then the three sides in the right triangle ODE are 1: 2: root number 5.

That is, radius: side length = root number 5: 2.

Espacio 2

BD*AD=DE = 100

BD+AD= diameter

In the right triangle ABC

(BD+AD) Party =(BD+4) Party +(AD+4) Party

(BD+4)(AD+4)=4(BD+AD)= triangle area *2

solve an equation

Note that (BD+AD) and BD*AD can be regarded as an unknown whole when solving equations.

BD+AD= diameter =2 1.