Isikhundla Semibuthano Emibili: Ukuhlaziywa Kwejiyometri
Kwezibalo, ikakhulukazi ku-geometry, ukuqonda indawo yezindilinga ezimbili kudlala indima ebalulekile. Izindilinga zingenye yezimo eziyisisekelo ze-geometric ezivame ukutholakala kuzo zombili izimfundiso kanye nezicelo ezisebenzayo. Indawo yezindilinga ezimbili inikeza ukuqonda ngokusebenzisana kwalezi zimo ezimbili lapho zibekwe endizeni. Lolu cwaningo luhlanganisa ukuhlaziywa kokuxhumana okuhlukahlukene okungenzeka kwenzeke, kusukela kokungaxhumani kuya ekuhlanganeni. Lesi sihloko sizobukeza ngokuphelele indawo yezindilinga ezimbili kanye nezici ezahlukahlukene ezihlobene.
Izincazelo kanye nemibhalo
Okokuqala, ake sichaze ngokusemthethweni imibuthano emibili endizeni yeCartesian. Indilinga \(C_1\) enesikhungo \(P_1(x_1, y_1)\) kanye nerediyasi \(r_1\) ingavezwa ngesibalo:
\[
C_1: (x – x_1)^2 + (y – y_1)^2 = r_1^2
\]
Ngokufanayo, indilinga \(C_2\) enesikhungo \(P_2(x_2, y_2)\) kanye nerediyasi \(r_2\) imelelwa yi:
\[
C_2: (x – x_2)^2 + (y – y_2)^2 = r_2^2
\]
Indawo yalezi zindilinga ezimbili incike ebangeni eliphakathi kwezikhungo zazo (\(d\)) kanye nobude be-radii yazo. Ibanga \(d\) eliphakathi kwezikhungo zezindilinga ezimbili \(P_1\) kanye \(P_2\) lingabalwa kusetshenziswa ifomula:
\[
d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
\]
Isigaba Sesikhundla Sendilinga Emibili
Ngokuvamile, kunezikhundla ezinhlanu ezingase zibhekane nazo le mibuthano emibili:
1. Ukuhlangana Kwezindilinga Ezimbili (Ukufana Kwezindilinga Ezimbili)
2. Ukungaphambani (okungafani nhlobo)
3. I-Tangent Yangaphandle
4. Ukuthinta Kwangaphakathi (I-Tangent Yangaphakathi)
5. Ukuhlangana
Isigaba ngasinye salezi sinezimo zaso zejometri, esizoxoxa ngazo ngokuningiliziwe ngezansi.
1. Ukuhlangana Kwezindilinga Ezimbili (Ukufana Kwezindilinga Ezimbili)
Izindilinga ezimbili zibhekwa njengezihambisanayo noma ezihambisanayo uma zinesikhungo esifanayo kanye nobubanzi obufanayo. Ngokwezibalo, lokhu kusho ukuthi:
\[
P_1 \equiv P_2 \quad \text{and} \quad r_1 = r_2
\]
Kulesi simo, \(d = 0\). Izindilinga ezimbili ziyafana, futhi iphuzu ngalinye kumbuthano owodwa liyiphuzu kwelinye imbuthano.
2. Ukungaphambani (okungafani nhlobo)
Kuthiwa iziyingi ezimbili azihlangani ngaphansi kwezimo ezimbili:
– Isimo Sokuqala: Uma ibanga eliphakathi kwezindawo ezimaphakathi zezindilinga ezimbili (d) likhulu kunesamba sobude be-radii yazo:
\[
d > r_1 + r_2
\]
– Isimo Sesibili: Uma indilinga eyodwa ingaphakathi kwenye indilinga ngaphandle kokuthinta nhlobo. Lokhu kwenzeka uma:
\[
d < |r_1 - r_2| \] Kuzo zombili izimo, akukho phuzu elifanayo phakathi kwezindilinga \(C_1\) kanye \(C_2\). 3. I-Tangent Yangaphandle Izindilinga ezimbili zi-tangent yangaphandle uma zithintana endaweni ethile futhi zingaphandle komunye nomunye. Lokhu kwenzeka uma ibanga eliphakathi kwezikhungo zezindilinga ezimbili lilingana nesamba se-radii yazo:
