The first question:

The key to this problem is how to represent AB in the equation.

According to Pythagorean theorem, AB= root sign (OA square +OB square).

According to the relationship between root and coefficient (also known as Vieta theorem), OA square +OB square =(OA+OB) square-2 (OA OB) =196-8 (AB+2) =180-8ab.

So if AB= radical sign (180-8AB), AB can be solved ~

Then the equation about x can also be solved ~

Then OA and OB have to come out ~

Finally, Tan Can asked ~

The second question:

First you have to get the equation of straight line AB ~

Then, set the coordinates of point P, which contains an unknown number, right ~

Furthermore, the coordinates of Q point can also be expressed by this unknown number.

The lengths of OQ, OA and PQ can be expressed by this unknown number respectively ~

According to the fact that the area of trapezoid and triangle is equal, we can use the formula "area = area" ~

Then, solve the unknown, P and Q coordinates can be found, and then all come out ~

The third question:

It is discussed in three situations, the first is MP, the second is PQ, and the third is MQ ~

Just look at whether the other two sides are equal in length.

I don't know how your grades are, but this question is really a bit difficult. Come on!

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