The Poncelet Simson-line envelope point conjecture

Let a Poncelet triangle family be inscribed in a circle. Fix a point $F$ on the circumcircle, let $V$ be the perpendicular projection of $F$ onto the Simson line of a member of the family, and let the Simson lines vary through the family. Simson-line envelope point conjecture. Over any Poncelet triangle family inscribed in a circle, the envelope of the Simson lines is a point $W$ antipodal to $F$ on the circular locus of $V$. The preceding theorem establishes that the locus of the projection $V$ is a circle, and the claim identifies the Simson-line envelope; its general validity is presented as an open conjecture.