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( 1)①t/9 = 1-t/6t = 18/5

②t/9=t/6- 1 t= 18

(2) If it is a diamond, it must be a parallelogram.

① when t = 18/5, AO=2, AQ = 0.4.

② When t = 18, point Q is at B, and AB = BO = 2. At this time, the quadrilateral AQOP is a diamond.

(3)① When t = 6 √ 3, AB = BP = 2, AB and BP can make a diamond with an included angle of 30.

② When t = 12-6 √ 3, make a diamond with AB and AP as adjacent sides and an included angle of 30.