How Can We Prove Quadrilateral Similarity Through Circle Intersections?

[SonyDvDPro]

Given a quadrilateral ABCD,
Prove that the quadrilateral formed by the intersections other than the vertices A, B, C & D
of the circles with diameter AB, BC, CD & DA
is similar to the quadrilaterar ABCD.

What is the relation of similarity?

 

[Mr.Brown]

similarity means just the same up to scale hence all angles are the same but the lenghts are different.

 

[mathman]

similarity means just the same up to scale hence all angles are the same but the lenghts are different.

The lengths of the sides scale together.