In 1 isosceles trapezoid ABCD, AD should be the upper sole and BC the lower sole.

The inscribed circle O cuts the waist AB at point N, the bottom AD at point E and the bottom BC at point F..

From the symmetry, we can get: na = AE = ed = DM = X.

NB=BF=FC=CM=y。

At the same time ∠C+∠D= 180? .

∴cos∠C+cos∠D=0.

2 In ⊿ADM, we can get from cosine theorem:

cos∠D=(AD？ +MD？ -Me? )/[2AD×MD]=(5x？ -Me? )/(4x？ ).

Namely: cos∠D=(5x? -Me? )/(4x？ ).

At ⊿BCM, you can also get:

cos∠C=(5y？ -BM？ )/(4y？ )

∴ Two types of addition and finishing can be obtained:

【AM？ /x？ ]+[BM？ /y？ ]= 10.

It is easy to know that point A is the point outside the inscribed circle O, AM is the secant of the circle O, and an is the tangent.

∴:x from the "Secant Theorem"? = Ann? =AK×AM。

∴AM/AK=AM？ /(AK×AM)=AM？ /x？ .

Similarly, y? =BN？ =BL×BM。

∴BM/BL=BM？ /(BL×BM)=BM？ /y？ .

∴ summary: AM/AK=AM? /x？ And BM/BL=BM? /y？ .

Generation: [AM? /x？ ]+[BM？ /y？ ]= 10.

Available: (AM/AK)+(BM/BL)= 10.