A. when p is on AO (2-3t is greater than or equal to 0)

Do AO vertical line QE passes through q and do AO vertical line CF passes through C.

Then QE/CF =OQ/OC

So QE=( 1/ root number 3)t divided by OC= (1/ root number 3)t divided by (2/ root number 3)=t/2.

Because OP=2-AP=2-3t(2-3t is greater than or equal to 0)

So S= 1/2 * QE *OP=-3t squared /4 +t/2(t is less than or equal to 2/3).

B when p is on OB (2-3t is less than or equal to 0, t is less than or equal to OC).

OP=3t-2 OQ=t angle BOC=90 degrees.

So S= 1/2 *OP*OC =3t squared /2 -t(2/3 less than or equal to t less than or equal to 2/ root number 3).

(2) Know the equation of straight line AB from A and B: y= (negative root number 3 )X+2 root number 3.

So let D( X, (negative root number 3 )X+2 root number 3)

A. when OC=OD=(2/ root number 3), it is obtained from the distance formula between two points:

The square of x+((negative root number 3 )X+2 root number 3) is 4/3.

You can solve X=, Y=. (a little hard to calculate)

B when DO=DC, an equation about x can be obtained from the distance formula between two points, which is a bit difficult to calculate. .

(3) It doesn't seem to scream

Let's talk about it. Set the angle, MCO. That's what MC AN means

Then use MC, AN an to represent 3 sides to find the circumference.

Ok, ok, I wish you a good result in the middle school entrance examination.