## Rotating a triangle in its circumcircle

Construct a triangle t'=(A'B'C') that can be rotated on its circumcircle with center O.
There are several possibilities to do that with EUC. Here is one that is quite stable under modifications.
1) Construct a triangle t=(ABC) which will be the prototype-triangle.
2) Construct its circumcircle with center Q.
3) Construct two points O and E.
4) Construct the circle with center O, passing through E.
5) Put a point A' ON the circle (OE). We will construct triangle t=A'B'C' similar to t.
5) Select the Angle tool: click on A ...drag ...release at Q then click again at B.
6) Click again at B ... drag ... release at Q, then click at C. Last two steps construct the angles <(AQB) and <(BQC).
These angles will be transfered to the other circle to produce triangle t' = A'B'C', similar to t.
7) Select the Angle-compasses tool and click on angle <(AQB), then click at A', then at O (pressing also CTRL). This defines <(A'OB').
8) Click now on angle <(BQC), then click at B', then at O. This defines <(A'OB').
9) Construct the triangle t'=(A'B'C').

In the construction described above, the following elements are movable:
1) FREE movable: triangle t = (ABC), points E and O.
2) ON CONTOUR movable: point A'.

To free move objects you switch to the selection-tool (Ctrl+1) and catch them.
To move-on-contour points you switch to the selection-on-contour-tool (Ctrl+2) and catch them.

Moving on contour the point A', makes the whole triangle t'=(A'B'C') rotate on its circumcircle.
Moving the vertices A,B,C changes the shape of the triangle t and its homothetic t' simultaneously.