Solution: According to the meaning of the question, the triangle ABC is an isosceles right triangle, the quadrilateral is just a square, and the center O is just a square.

The center of the shape is the center of AC. It is also known that AB=BC=8,

Because CP=2 and AP=6. According to the pythagorean theorem of right triangle, it is concluded that AP= 10, so BQ= 10.

Because triangle ABP and triangle ABR

So triangle ABP and triangle ABR are congruent triangles, then < ABR = & ltBAP so AQ=BQ.

Draw a vertical line to AB after crossing Q, and cross AB and G, then G is the center of AB, and AG= 1/2AB=4.

At the triangle headquarters base, because

In triangle AGP, cos

because

Then QR=BR-BQ=5.

So: BQ/QR=5/5= 1.