Xin Li, a poet in the Tang Dynasty, said in the first two sentences of his poem "An Ancient Warsong": "Climb mountains during the day and watch the fire on the top of the mountain. At yellow dusk, we

Xin Li, a poet in the Tang Dynasty, said in the first two sentences of his poem "An Ancient Warsong": "Climb mountains during the day and watch the fire on the top of the mountain. At yellow dusk, we drink horses in the river on the border." There is an interesting number in this poem. (1)∵ In the isosceles trapezoid ABCD, AB=CD=AD=2, ∠ D = 120, and points E and F are the midpoint of the base AD and BC respectively.

∴∠DAC=∠DCA=30，

∴∠ACB=30，

∴∠BAC=90，

∴tan∠ACB= exchange company,

∴AC= 2 3 3 = 2 3，

So the answer is: 2 3;

(2) As shown in the figure, if point A is the symmetrical point A' about MN, then A' is on ⊙O,

When BP ′+AP ′ is minimum, connect Ba ′ intersection MN at P ′.

According to symmetry, AP ′ = a ′ p ′,

∴bp′+ap′=bp′+a′p′=a′b，

Connect OA, OB, OA',

It is known that arc AN= arc A'n,

Then ∠ NOA' = ∠ NOA = 2 ∠ m = 60,

Point b is that midpoint of arc AN,

∴∠BON=30

∴∠boa′=90

And MN= 1,

∴ in RT △ OA ′ b, A ′ b = 22.

That is, the minimum value of BP+AP is 2 2.

(3) ① The symmetry axis y of ∫ parabola = AX2+BX+C (A ≠ 0) is x= 1, and the parabola passes through A (- 1, 0).

C(0, -3) two points, respectively, into the second resolution function:

∴ - b 2a = 1 a-b+c=0 c=-3，

Solution: a= 1, b=-2, c=-3,

The quadratic resolution function is y=x 2 -2x-3,

② Get the straight line BC: y = x-3,

∴M( 1, -2), the length of AC is: 10.

∴△△△ The minimum perimeter of ACM is the minimum value of AM+CM.

∫AM+CM = BC = 3 ^ 2，

∴△△△ The minimum circumference of ACM is: 10+32.