That the angle of S(D), S(E) is a right one follows from the discussion in SimsonProperty2.html .

The proof of the other statement follows from the fact that the orthocenter H of t is the similarity center of the Euler circle and the circumcircle of t. To complete the argument draw parallels to S(D), S(E) intersecting at point G on (c). From SteinerLine.html follows that the intersection point F of S(D) and S(E) and the intersections J, I of these lines with HD, HE make a triangle s = IJF, similar to DEF etc. Notice, by the way that diameter IJ of the Euler circle is parallel to the diameter DE of the circumcircle c.

SimsonGeneral.html

SimsonGeneral2.html

SimsonProperty.html

SimsonProperty2.html

Simson_3Lines.html

SimsonVariantLocus.html

SteinerLine.html

ThreeDiameters.html

ThreeSimson.html

TrianglesCircumscribingParabolas.html

WallaceSimson.html

Produced with EucliDraw© |