Parabolas Associated with a Triangle

Artzt parabolas of a triangle

“…Bullard wrote two papers in 1935 and 1937 [2,3] (without mentioning Artzt) which are the best source for the many remarkable properties of these parabolas. Further properties were also given by Thébault in 1957 [16] but other references are hard to find. Figure 7 shows the configuration for the three parabolas of the first type, but to find more properties we need to draw the medians as shown in Figure 8.…”

“…The papers by Bullard [2,3] and Thébault [16] together with the French nineteenth century ones contain other properties of which the following are worth pointing out. The second type of parabolas seems to be mentioned sparsely in the literature.…”

Triads of Conics Associated with a Triangle

“…Triads of "Artzt" parabolas, conceived in the XIX century, have been revisited in [4,9,15]. In [13], new properties of Artzt parabolas are detected via dynamic geometry software.…”