Solve a math fill-in-the-blank problem in Jingzhou senior high school entrance examination 20 1 1

Extend the X axis of BC intersection to E, because ∠ ABC = 90, AB//OD, ∠ CEO = 90.

Because CO shares ∠AOD, ∠COE=∠COB 1,

Because △ABC is folded along AC to get △ACB 1, △ ABC △ ACB1.

So ∠ CB 1o = ∠ ABC = ∠ CEO = 90, CB 1=CB.

Add CO=CO to get △ Coe△ cob1,

So CB 1=CD.

Let the coordinate of C be (a, 2/a), then CB=CB 1=CD=2/a, and the coordinate of B is (a, 4/a).

So the ordinate of a is 4/a, and the coordinates of a (a/2, 4/a) are obtained.

S△cob 1 = S△COD = 1/2 * a *(2/a)= 1

S△ACB 1 = S△ABC = 1/2 *(a-a/2)*(4/a-2/a)= 1/2

So the area of the quadrilateral OABC = 1+ 1/2*2=2.