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Brocard Points of the Triangle

Given three points A, B and C,
find the point P such that angle(PAB) = angle(PBC) = angle(PCA).
Express tan(PAB) in terms of A, B and C.
construction of P
calculation of tan(PAB)
the other point P
coordinates of P

java applet or image[Java applet]

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The construction makes frequent use of Euclid III 32
Click and drag A, B or C to modify the picture.
Click and drag any other point to move the picture.