suntee vruttam

jyaamitiloo, tribhujam yokka chuttupakkala vruttam ledhaa chuttupakkala vruttam anedi moodu sheershaala gundaa vellae vruttam. eee vruttam yokka kendraanni tribhujam yokka chuttukolata anie pilustaaru, mariyu daani vyaasaarthaanni chuttukolata anie pilustaaru. tribhujam yokka vaipula moodu lamba dvibhaagaala madhya koodali binduvu circanter, mariyu idhi tribhuja kendram.
marinta saadhaaranamgaa, oke vruttamlo anni sheershaalato kuudina oka-vaipu bahubhujanni, chuttumuttina vruttam anie kooda pilustaaru, dheenini chakriya bahubhujamgaa ledhaa pratyeka sandarbhamlo, chakriya chaturbhujamgaa pilustaaru. anni deerghachaturasraalu, isocels trapezoids, kudi galipatalu mariyu saadhaarana bahubhujalu chakreeyamgaa untaayi, conny prati bahubhuji kaadu.
strait edge mariyu kampas nirmaanam.
tribhujam yokka chuttukolatanu moodu lamba dvibhagalalo edainaa rendintini geeyadam dwara nirminchavacchu. moodu naan-collinear paayintla kosam, eee rendu panktulu samaantaramgaa undavu, mariyu chuttukolata anedi avi daate sthaanam. dwibhaajakampai unna edainaa binduvu adhi dwibhajitamayye rendu binduvula nundi samaana dhooramlo untundi, dheeni nundi eee binduvu, rendu dvibhaajakaalu, moodu tribhuja sheershaala nundi samaana dhooramlo untundi.
circramedius anedi daani nundi moodu sheershaalalo deenikainaa unna dhooram.
pratyaamnaaya nirmaanam.
chuttukolatanu nirnayinchadaaniki oka pratyaamnaaya paddhati emitante, oka vertices nundi oka konam vadda oka saadhaarana vaipu nundi bayaludere edainaa rendu rekhalanu geeyadam, bayaludere saadhaarana konam 90° mainus vyatiraeka vertex konam. (vyatiraeka konam aspashtamgaa unna sandarbhamlo, pratikuula konamlo oka rekhanu geeyadam antey tribhujam velupala velladam.)
teerapraanta naukayanamlo, tribhujam yokka chuttukolata konnisaarlu diksuchi andubaatulo lenappudu sextant upayoginchi sthaana rekhanu pondhe maargamgaa upayoginchabadutundi. rendu mailuraalla madhya kshitija samaantara konam pariseelakudu unna sarkilnu nirvachistundi.
circle sameekaranaalu.
cartician coordinatelu.
euclidean samatalamlo, chekkabadina tribhujam yokka sheershaala cartician akshaamsaala paramgaa suntee vruttam yokka sameekaranaanni spashtamgaa ivvadam saadhyamavutundi. anukundam
avi paayintla akshaamsaalu. circle appudu cartician plain loe paayintla formula _ 2 yokka locus sameekaranaalanu santruptiparustundi
vruttam yokka saadhaarana kendra suutram _ 4 nundi anni paayintlu oke dhooramlo unnayani haamii ivvadam. dhruveekarana gurtimpunu upayoginchi, eee sameekaranaalu maatrika yokka sthithiki taggutaayi
dheeniki sunna kaani kernell untundi. anduvalla sarkilnu pratyamnaayamgaa eee maatrika yokka nirnayaadhikaari yokka sunnaala sthaanamgaa varninchavachhuh
cofactor vistarananu upayoginchi,
appudu manaku suutram _ 8 untundi, ikkada suutram _ 9 mariyu-moodu paayintlu oka rekhalo levani bhaavinchi (lekapothe suntee anedi anantam vadda unna saadhaaraneekarinchina vruttamgaa kooda chudagala rekha)-suutram _ 10
mariyu madhya antargata konam ekkada undhi. chuttukolata, dwara ivvabadutundi
eee suutram moodu kolatalalo matrame panichestundi, endukante cross utpatti itara kolatalalo nirvachinchabadaledu, conny cross utpattulanu eee krindi gurtimpulatoe bharti cheyadam dwara itara kolatalaku saadhaaraneekarinchavachchuh
chuttukolata akshaamsaalu.
cartician coordinatelu.
circanter suutram _ 13 yokka cartician akshaamsaalu 
thoo 
saadhaaranatanu kolpokunda, cartician samanvaya vyavasthala muulaaniki sheersham yokka anuvaadam tarvaata dheenini saralikruta roopamlo vyakteekarinchavachhu, i.ii.eee sandarbhamlo suutram _ 16 unnappudu, sheersha suutram _ 17 mariyu suutram _ 18 yokka akshaamsaalu sheersham nundi eee sheershaalaku vaahakaalanu suuchistaayi. eee chinna anuvaadam anni tribhujaalaku saadhyamani gamaninchandi mariyu tribhujam yokka chuttukolata suutram _ 19 ilaa anusaristundi
thoo 
vertex yokka muulam yokka anuvaadam kaaranamgaa, circumradiusnu ilaa lekkinchavacchu
tribhujam yokka bhujaala podavulu ekkada unnaayi mariyu suutram _ 23 anedi ardhaparimiti. paina unna vyakteekarana suutram _ 24 anedi tribhujam yokka vaisaalyam, herron suutram dwara. circle yokka vyaasam kosam trikonamiti vyakteekaranalu unnaayi
tribhujam yokka tommidi-paayintla vruttam vruttam yokka sagam vyasanni kaligi untundi.
edainaa tribhujamlo, chuttukolata ellappuduu centroid mariyu orthocentertho calineerga untundi. vaatanninti gundaa vellae rekhanu euler line antaaru.
circanter yokka isogonal conjugate anedi orthocenter.
moodu paayintla yokka upayogakaramaina kaneesa sarihaddu vruttam anedi circle (ikkada moodu paayintlu kaneesa sarihaddu vruttamlo untaayi) ledhaa tribhujam yokka podavaina vaipu yokka rendu paayintla dwara nirvachinchabadutundi (ikkada rendu paayintlu vruttam yokka vyasanni nirvachistaayi). kaneesa sarihaddu vruttaanni suntee vruttamtoe gandaragolaniki guricheyadam sarvasaadhaaranam.
moodu collinear paayintla circle anedi moodu paayintlu unna rekha, dheenini tarachugaa "ananta vyaasaartham yokka vruttam" anie pilustaaru. daadaapu collinear paayintlu tarachugaa circle yokka gananalo sankhya asthirataku daariteestaayi.
tribhujaala yokka suntee vruttaalu paayintla samiti yokka delone tribhujamtho sannihita sambandhaanni kaligi untaayi.
jyaamitiloo euler siddhaantam prakaram, chuttukolata mariyu prothsaahaka madhya dhooram
ikkada vruttaakaara vyaasaartham mariyu vruttaakaara vyaasaartham; anduvalla vruttaakaaramu kaneesam rendu retlu vyaasaartham (euler yokka tribhujam asamaanata), samaanatvamto samabahu vishayamlo matrame.
orthocenter mariyu madhya dhooram
centroid mariyu tommidi-paayintla center kosam manaku undhi
oka tribhujam yokka chuttupakkala vyaasaartham mariyu chuttupakkala vyaasaartham yokka gunakam
circradius, vaipula mariyu meediyanlatho, manaku undhi
madhyastha, etthu mariyu antargata dvibhaajakaalu annee tribhujam yokka oke sheersham nundi circradiusto udbhaviste, appudu
carnot siddhaantam prakaram, chuttukolata nundi moodu vaipula unna dhooraala mottam circumradius mariyu inradius mottaaniki samanam. ikkada oka vibhagam yokka podavu tribhujam velupala puurtigaa unte matrame pratikuulamgaa pariganinchabadutundi.
oka tribhujaaniki daani vruttam mariyu vruttam vale rendu pratyeka vruttaalu unte, adhe vruttam mariyu vruttam gala anantamaina itara tribhujaalu unnaayi, vruttam meeda edainaa binduvu sheersham vale untundi. (idhi ponsellet yokka porism kesu). atuvanti tribhujaalu undataaniki avasaramaina mariyu taginanta sharatu paina perkonna samanatva suutram.
chakriya bahubhujalu.
oke vruttamlo unna binduvula samitini "concyclic" anie pilustaaru, mariyu shrungaalu concyclic ayina bahubhujanni "cyclic bahubhuji" anie pilustaaru. prati tribhujam chakreeyamgaa untundi, conny moodu kante ekkuva vaipula unna bahubhujalu saadhaaranamgaa undavu.
chakriya bahubhujalu, mukhyamgaa naalugu vaipula chakriya chaturbhujaalu, vividha pratyeka lakshanaalanu kaligi untaayi. mukhyamgaa, chakriya chaturbhujaaniki vyatiraeka koonaalu anubandha koonaalu (180° ledhaa π raediyanlanu jodinchadam).

