(In reply to
re: GSP exploration by Charlie)
It looks like, when segment BC is closer to the center of the circle than 1/3 the radius, the constructed hyperbola encloses the original circle within one of its nappes. When chord BC is farther than 1/3 of the radius away from the center, one of the nappes intersects the circle in two points. At 1/3 radius distance from the center one nappe is tangent to the circle on the side closer to the other nappe.
The center of the circle seems always to be within the "moving" nappe, getting more pointy as the chord BC gets farther from the circle center.

Posted by Charlie
on 20171213 15:24:45 