The generalized Simson lines, for various positions of the point J on the circumcircle of ABC, envelope a deltoid [d] similar to the envelope of the Simson lines of ABC. The tangent circle of [d] is equal to the Miquel circle of points J, L, M, etc. (look at SimsonGeneral.html ). This tangent circle results by applying a spiral similarity F on the Euler circle of ABC (is tangent to the corresponding deltoid). F has center at the circumcenter L of ABC, angle of rotation (psi) = (pi)/2 - (phi) and modulus 1/cos(psi) = LR/LK.

Simson.html

SimsonDiametral.html

SimsonGeneral.html

SimsonProperty.html

SimsonProperty2.html

Simson_3Lines.html

SimsonVariantLocus.html

SteinerLine.html

ThreeDiameters.html

ThreeSimson.html

TrianglesCircumscribingParabolas.html

WallaceSimson.html

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