Figure 8 - uploaded by Dan Reznik

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# The circles passing through a cusp P i , its pre-image Pi, and M osculate E at the Pi. The centers P i of said circles define a triangle T (dashed black) whose area is constant for all M . X 2 denotes its (moving) barycenter. Video: [10, PL#03,#05].

Source publication

The Negative Pedal Curve (NPC) of the Ellipse with respect to a boundary point M is a 3-cusp closed-curve which is the affine image of the Steiner Deltoid. Over all M the family has invariant area and displays an array of interesting properties.

## Contexts in source publication

**Context 1**

... Each of the 3 circles passing through M, P i , P i , i = 1, 2, 3, osculate E at P i , Figure 8. Their centers define an area-invariant triangle T which is a half-size homothety of T . ...

**Context 4**

... Each of the 3 circles passing through M, P i , P i , i = 1, 2, 3, osculate E at P i , Figure 8. Their centers define an area-invariant triangle T which is a half-size homothety of T . ...

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