Li-circles le Tangents: Mehopolo, Litšobotsi le Litšebeliso
Selikalikoe ke sebopeho sa jeometri se thehiloeng holim'a mothapo o bonolo o koetsoeng. Lilikalikoe li na le litšobotsi tse fapaneng tse khahlisang tse 'nileng tsa ithutoa ka lipalo ka makholo a lilemo. Khopolo e 'ngoe ea bohlokoa e amanang le lilikalikoe ke mola oa tangent. Sehlooho sena se tla tšohla hore na lilikalikoe le tangent ke eng, litšobotsi tsa tsona, le ts'ebeliso ea likhopolo tsena masimong a fapaneng.
Tlhaloso ea Selikalikoe
Ho ya ka dipalo, sedikadikwe se hlaloswa e le sete ya dintlha tsohle tse ka hara sefofane tse leng sebaka se tsitsitseng ho tloha ntlheng e itseng, se bitswang setsi sa sedikadikwe. Sebaka sena se tsitsitseng se tsejwa e le radius ya sedikadikwe. Setshwantsho sa aljebra sa sedikadikwe hangata se fanwa ka sebopeho:
\[ (xh)^2 + (yk)^2 = r^2 \]
Tekanyong ena, (h, k) ke likhokahano tsa bohareng ba selikalikoe 'me r ke radius ea eona.
Matlotlo a Li-circles
1. Ho Tsitsisa ho Potolohang: Selikalikoe ke sebopeho se lekanang ka li-axe tsohle tse fetang bohareng ba sona, ho bolelang hore se lula se sa fetohe ha se potoloha.
2. Botsitso ba Boholo: Selikalikoe sa selikalikoe le sebaka sa sebaka se koetsoeng ke selikalikoe li na le foromo e tsitsitseng, e leng:
– Selikalikoe = \( 2 \pi r \)
– Sebaka = \( \pi r^2 \)
3. Sebaka sa Sekhutlo: Sedikadikweng, sekhutlo se sekametseng ke arc kahare ho sedikadikwe bohareng ba sedikadikwe se feta sekhutlo se sekametseng ka ntle ho sedikadikwe habeli (ho etsa kgutlotharo ya isosceles).
Tlhaloso ea Mohala oa Tangent
Tangent ho selikalikoe ke mola o amang selikalikoe ntlheng e le 'ngoe feela. Ntlha ena e tsejoa e le ntlha ea tangency. Thepa ea bohlokoa ea tangent ke hore e otlolohile ho radius ea selikalikoe e fetang ntlheng ea tangency.
Ho ya ka dipalo, haeba re na le mola o nang le equation \( y = mx + c \) o amang sedikadikwe \( (xh)^2 + (yk)^2 = r^2 \) ntlheng e nngwe, mola o na le sebopeho se otlolohileng ho sedikadikwe haeba feela:
\[ (h + mr – k)^2 = r^2 (1 + m^2) \]
Matlotlo a Tangents
1. E otlolohile ho ea ho Radius: Ha e le moo ho otlolohileng, mola o otlolohileng o lula o otlolohile ho ea ho radius ea selikalikoe.
2. Ntlha e le 'Ngoe ea Tangency: Mola o nang le tangent o ama selikalikoe ntlheng e le 'ngoe feela.
3. Bolelele ba Karolo ea Mola: Haeba ho huloa li-tangent tse peli ho tloha ntlheng e le 'ngoe ea kantle ho ea selikalikoeng, bolelele ba karolo ho tloha ntlheng e ka ntle ho ea ntlheng ea tangency boa tšoana.
Tšebeliso ea Li-circles le Tangents
1. Litsela tse kholo le Meralo ea Motheo
Tšebeliso e le 'ngoe ea li-tangent e ka bonoa moralong oa litsela tse kholo, haholo-holo likhutlong le likoung tsa litsela. Tšebeliso ea li-circles le li-tangent meralong ena e thusa ho netefatsa hore likoloi li fetoha ka tsela e boreleli le e sireletsehileng.
2. Bolepi ba linaleli le jeokrafi
Liketsahalo tse ngata tsa bolepi ba linaleli le tsa jeokrafi li sebelisa molao-motheo oa li-circles le li-tangent, mohlala, litsela tse potolohang tsa lipolanete tse batlang li le chitja, le mela ea terminator Khoeling le lipolaneteng ho hlalosa karohano ea motšehare le bosiu.
3. Meaho
Li-circle le li-tangent li sebelisoa khafetsa meahong ho theha likarolo tsa botle le meaho e sebetsang hantle. Matlo le lifensetere tse chitja ke mehlala e meng ea ts'ebeliso ena.
4. Liroboto
Didikadikwe le di-tangent di sebediswa dirobotong bakeng sa ho tsamaya le ho etsa dimmapa. Di-sensor tsa LiDAR (Light Detection and Ranging) di sebedisa didikadikwe ho lemoha bohole ba dintho tse di potileng.
5. Setso le Bonono
Li-circles li fumanoa hangata matšoao le bononong ho pholletsa le litso tse fapaneng. Li-tangent li sebelisoa meralong e fapaneng ea bonono ho etsa lipaterone le phapang ea pono.
6. Mabone
Ho optics, melao-motheo ea li-circle le tangents e sebelisoa ho rala lilense tsa boleng bo holimo. Lilense tse kobehileng le tse kobehileng li sebetsa ka ho sebelisa melao-motheo ena ho tsepamisa leseli.
Ho Rarolla Mathata ka ho Sebelisa Maqheka
Di-tangent di sebediswa kgafetsa mathateng a fapaneng a jeometri. Mohlala, ho fumana bolelele ba mola o nang le tangent ho tloha ntlheng e ka ntle ho ya ntlheng ya tangency, kapa ho fumana sekhutlo pakeng tsa di-tangent tse pedi. Mohlala wa bothata ba jeometri ke ona:
Potso: Fanoa ka selikalikoe se nang le equation \( (x-3)^2 + (y+4)^2 = 25 \). Fumana equation ea mola o tangent ntlheng (6, 0).
Tharollo:
1. Ho Fumana Radius ea Selikalikoe: Ho tsoa ho equation ea selikalikoe, re ka bona hore radius ke \( r = 5 \) 'me setsi sa selikalikoe se ho \( (3, -4) \).
2. Ho Fumana Radius Gradient: Gradient ea radius ho tloha bohareng (3, -4) ho ea ntlheng (6, 0):
\[ m = \frac{0 – (-4)}{6 – 3} = \frac{4}{3} \]
3. Gradient ea Mola o Tangent: Mola o tangent o otlolohile ho radius, kahoo gradient ea oona ke e fapaneng le gradient ea radius. Gradient ea mola o tangent ke \( m = -\frac{3}{4} \).
4. Ho Sebelisa Khokahano ea Mela: Ho sebelisoa ntlha (6, 0) le gradient -3/4 ho khokahano ea mela \( y – y_1 = m (x – x_1) \):
\[ y – 0 = -\frac{3}{4} (x – 6) \]
\[ y = -\frac{3}{4}x + 4.5 \]
Kahoo, equation ea mola oa tangent ke \( y = -\frac{3}{4}x + 4.5 \).
Qetello
Didikadikwe le di-tangent ke dikgopolo tsa motheo thutong ya jeometri tse nang le thepa e mengata e kgahlehang le ditshebediso tse sebetsang. Hase feela karolo e tebileng ya dipalo tsa thuto empa hape ke disebediswa tsa bohlokwa mafapheng a tlohang boenjiniereng ho ya ho bonono. Kutlwisiso e tiileng ya dikgopolo tsena e bula monyako wa boqapi le ditharollo tsa mathata a letsatsi le letsatsi.
Jwalo ka ha re se re hlahlobile sehloohong sena, botle ba dipalo bo hodima ditshebediso le ditshebediso tsa tsona tse re dumellang ho tjheka ka botebo le ho fumana ditharollo tse ntle dikarolong tse fapaneng tsa bophelo.
