How Can We Prove Quadrilateral Similarity Through Circle Intersections?

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SonyDvDPro
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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?
 

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