Miquel circle

Given a triangle abc, 3 in line points X,Y,Z and a point P,
construct a triangle ABC directly similar to abc, whose sides go through X,Y and Z
and whose circumcircle goes through P.
Precisely we want ABZ in line, BCX in line and ACY in line, to be shure which point is on which side.
Hint

Details (Includes Java applet, please wait...)

 

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