Muchinyorwa chino, tichatarisa imwe yezvidzidzo zvekare zve affine geometry - theorem yeCeva, iyo yakagamuchira zita rakadaro mukukudza injiniya weItaly Giovanni Ceva. Tichaongororawo muenzaniso wekugadzirisa dambudziko kuitira kuti tisimbise zvinyorwa zvinoratidzwa.
Chirevo che theorem
Triangle yapiwa ABC, umo vertex imwe neimwe yakabatana kune imwe nzvimbo kune rimwe divi.
Saka, tinowana zvikamu zvitatu (AA', BB' и CC'), vanonzi cevians.
Izvi zvikamu zvinopindirana pane imwe nguva kana uye chete kana kuenzana kunotevera kuchibata:
|UYE'| |KWETE'| |CB'| = |BC'| |SHIFT'| |AB'|
Iyo theorem inogona zvakare kuratidzwa mune iyi fomu (inotemerwa muchiyero chipi icho mapoinzi anopatsanura mativi):
Ceva's trigonometric theorem
Cherechedza: makona ose akatariswa.
Muenzaniso wedambudziko
Triangle yapiwa ABC nemadotsi KUNA', B' и VS ' kumativi BC, AC и AB, zvichiteerana. Iwo ma vertices egonyo akabatana kune akapihwa mapoinzi, uye zvikamu zvakaumbwa zvinopfuura nepoindi imwe. Panguva imwe chete, pfungwa KUNA' и B' inotorwa pakati pemativi anoenderana akapesana. Tsvaga muchiyero chei poindi VS ' inopatsanura rutivi AB.
mhinduro
Ngatidhirowe dhirowa zvinoenderana nemamiriro edambudziko. Kuti tive nyore, tinotora chinyorwa chinotevera:
- AB' = B'C = a
- BA' = A'C = b
Izvo zvinongosara kunyora chiyero chezvikamu zvinoenderana neCeva theorem uye kutsiva iyo yakagamuchirwa notation mairi:
Mushure mekudzikisa zvikamu, tinowana:
Nokudaro, AC' = C'B, kureva point VS ' inopatsanura rutivi AB nehafu.
Naizvozvo, mumatatu edu, zvikamu AA', BB' и CC' vari vepakati. Tapedza dambudziko, takaratidza kuti vanopindirana pane imwe nguva (inoshanda kune chero katatu).
Cherechedza: vachishandisa theorem yaCeva, munhu anogona kuratidza kuti mune katatu pane imwe nguva, bisectors kana kureba zvinopindirana.