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The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...

For a triangle DeltaABC and three points A^', B^', and C^', one on each of its sides, the three Miquel circles are the circles passing through each polygon vertex and its ...

The lines AK_A, BK_B, and CK_C which are isogonal to the triangle medians AM_A, BM_B, and CM_C of a triangle are called the triangle's symmedian. The symmedians are ...

The catacaustic of the natural logarithm lnx specified parametrically as x = t (1) y = lnt (2) is a complicated expression for an arbitrary radiant point. However, for a ...

The plane curve given by the equation xy=x^3-a^3, illustrated above for values of a ranging from 0 to 3. For a=0, the trident degenerated to a parabola.

The line segment KO^_ joining the symmedian point K and circumcenter O of a given triangle. It is the diameter of the triangle's Brocard circle, and lies along the Brocard ...

A circumconic hyperbola, which therefore passes through the orthocenter, is a rectangular hyperbola, and has center on the nine-point circle. Its circumconic parameters are ...

A pivotal isotomic cubic is a self-isotomic cubic that possesses a pivot point, i.e., in which points P lying on the conic and their isotomic conjugates are collinear with a ...

Consider a horse rider who wishes to feed his horse at a field, gather water from a river, and then return to his tent, all in the smallest overall distance possible. The ...

The circumcircle is a triangle's circumscribed circle, i.e., the unique circle that passes through each of the triangle's three vertices. The center O of the circumcircle is ...