Izvleček
V raziskovalni nalogi, ki sva jo napisali še kot učenki 9. razreda OŠ Dravlje, sva preučevali lastnosti trikotnika, ki je bil na določen način pričrtani poljubnemu trikotniku. Ugotavljali sva, na kakšen način sta pričrtani in izhodiščni trikotnik povezana, ter dokazovali različne izreke. Obravnavali sva sedem takih trikotnikov, in sicer Feurbachov trikotnik, medialni ali središčni trikotnik, nožiščni ali pedalni trikotnik, ortocentrični trikotnik, Napoleonov trikotnik, Miquelov trikotnik in Brocardov trikotnik. Pri vsakem izmed omenjenih trikotnikov sva izpostavili nekaj njihovih zanimivih lastnosti in dokazali nekaj trditev (matematičnih resnic). V pričujočem članku bova predstavili Feurbachov in Miquelov trikotnik ter Miquelove točke. Meniva, da sta ta dva najbolj zanimiva za branje in da so o ostali vsebini osnovnošolci in srednješolci že nekaj slišali ali prebrali. Vse konstrukcije sva risali s programom za dinamično geometrijo Geogebra.
Abstract
Triangles Drawn to a Triangle
The research paper, which we wrote in the 9th grade of the Dravlje Primary School, deals with the characteristics of a triangle which is joined with a random triangle in a certain way. We tried to find out the connections between the joined and the original triangle and prove different theorems. We chose seven triangles: the Feuerbach triangle, medial triangle, pedal triangle, orthocentric triangle, Napoleon triangle, Miquel triangle and the Brocard triangle. Each of the above-mentioned triangles is unique; therefore, we focused on their interesting characteristics and proved a few mathematical statements/truths. In the article we present the Feuerbach triangle, the Miquel triangle and the Miquel points. We believe that these two triangles make for interesting reading and that primary and secondary school students have already heard or read a little about the other triangles. All the constructions were drawn with the dynamic mathematics software Geogebra.