Dap an thi chon hoc sinh du thi homc lan thu 10 2013

From , we implies So Hence, we get By Thales theorem, we have A That is... From , interchanging with gives Solving the system, we get 7.. The isosceles triangle has Therefore AE =12cm.

DA PHUC HIGH SCHOOL MATHS TEST

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SOLUTION

then

That is

3 From , we implies

So

Hence, we get

By Thales theorem, we have A

That is B D C

6 From , interchanging with gives

Solving the system, we get

7 We have

=

=

So we get the desired result

x

A

D

E B C

Chose a point D on AE such that AD = AB = 3cm The isosceles triangle has

Therefore AE =12cm

9 We have (by the Cauchy inequality)

Similarly, we also have

The inequality is proved

10

From (*), we get