The idea is to rotate a fixed triangle t'=(A'B'C') in its circumcircle (center O) and rotate also another point (D) about O with a multiple (f=3) of the rotation velocity of t'. Then construct the projections (A'',B'',C'') of D on the sides of t' and get the circumcenter P of the triangle t''=(A''B''C''). The Geometric locus of P is the red line.

In the construction described below, the following elements are movable:

1) FREE movable: the triangle t= (ABC) and the points O and E.

2) ON CONTOUR movable: points A (on circle (OE) ) and D (on Line OD).

3) VARIABLE is also the number-object (factor f) which gives the angle-ratio <(EOD) over <(EOA').

To free move the points you switch to the selection-tool (Ctrl+1) and catch them.

To move-on-contour the points you switch to the selection-tool (Ctrl+2) and catch them.

To vary the factor f, click on it to select it and play with the up/down arrows on the keyboard.

Up to homothety, the shape of the locus depends

a) on the triangle-prototype t = (ABC),

b) on the factor f, and

c) on the distance |OD|.

The construction of a triangle, totating in its circumcircle is described in the file: RotatingTriangle.html .

For the construction of the multiple y=f*x of an angle, using a number-object (to represent f), look at the file: AngleMultiple.html .

Projection_Triangle.html

Simson.html

SimsonDiametral.html

SimsonGeneral.html

SimsonGeneral2.html

SimsonProperty.html

SimsonProperty2.html

Simson_3Lines.html

SteinerLine.html

ThreeDiameters.html

ThreeSimson.html

TrianglesCircumscribingParabolas.html

WallaceSimson.html

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