Geometric Construction 6

Construct
the part of the tangent of the deltoid intercepted by the curve.

Construct
two mutually orthogonal tangents of the deltoid. Where do they meet?

Construct
two mutually orthogonal normals of the deltoid. Where do they meet?

Construct
an animation displaying a deltoid sliding along two orthogonal straight
lines.

Construct
the family of Simson lines to a given triangle.

Discover a theorem about the Simson line and four points of a circle.

Discover a theorem about the Simson line and five points of a circle.

If a point M of a circle O is projected upon the four Simson lines of M
for the four triangles determined by the vertices of the quadrilateral
inscribed in O taken three at a time, what can be said about these four
projections? Formulate a new definition. Can you generalize this process?

Construct
a deltoid tangent to the sides of a given triangle.