Solution: connect AC and BP, AC and BD intersect at O.

Because the side length of the square ABCD is 1.

Therefore: AC⊥BD, OA = OC = √ 2/2.

Because s △ BCE = s △ PBE+s △ PBC, PQ ⊥ BC, PR ⊥ Be.

So: 1/2? Is it? OC= 1/2？ Is it? PR+ 1/2？ BC? Perceptual quantization

Because BE=BC

Therefore: OC=PR+PQ=√2/2.