Ọnọdụ nke okirikiri abụọ: Nyocha nke Geometric
Na mgbakọ na mwepụ, ọkachasị na geometry, nghọta nke ọnọdụ okirikiri abụọ na-arụ ọrụ dị oke mkpa. Okirikiri bụ otu n'ime ọdịdị geometry bụ isi a na-ahụkarị ma na tiori ma na ojiji bara uru. Ọnọdụ nke okirikiri abụọ na-enye nghọta banyere mmekọrịta nke ọdịdị abụọ a mgbe etinyere ya n'elu. Ọmụmụ ihe a gụnyere nyocha nke mmekọrịta dị iche iche nwere ike ime, site na enweghị njikọ ruo na njikọ. Isiokwu a ga-enyocha ọnọdụ nke okirikiri abụọ na akụkụ dị iche iche metụtara ya nke ọma.
Nkọwa na Ndetu
Nke mbụ, ka anyị kọwaa okirikiri abụọ n'usoro Cartesian plane. Enwere ike igosi okirikiri \(C_1\) nwere etiti \(P_1(x_1, y_1)\) na radius \(r_1\) site na nha nhata:
\[
C_1: (x – x_1)^2 + (y – y_1)^2 = r_1^2
\]
N'otu aka ahụ, okirikiri \(C_2\) nwere etiti \(P_2(x_2, y_2)\) na radius \(r_2\) nọchiri anya ya:
\[
C_2: (x – x_2)^2 + (y – y_2)^2 = r_2^2
\]
Ọnọdụ okirikiri abụọ a dabere na anya dị n'etiti etiti ha (\(d\)) na ogologo radii ha. Enwere ike ịgbakọ anya dị n'etiti etiti okirikiri abụọ ahụ (P_1\) na \(P_2\) site na iji usoro a:
\[
d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
\]
Nkeji Ọnọdụ Gburugburu Abụọ
N'ozuzu, e nwere ọnọdụ ise nke okirikiri abụọ ahụ nwere ike inwe:
1. Ihe dakọtara (Okirikiri abụọ dakọtara)
2. Anaghị ejikọta ọnụ (nke na-anaghị ekewapụ onwe ya)
3. Tangent Mpụga
4. Mmetụ Aka Dị n'Ime (Mgbawa Dị n'Ime)
5. Ịgafe
Nke ọ bụla n'ime ụdị ndị a nwere ọnọdụ geometric nke ya, nke anyị ga-atụle n'ụzọ zuru ezu n'okpuru.
1. Ihe dakọtara (Okirikiri abụọ dakọtara)
A na-ewere okirikiri abụọ dị ka ihe dakọtara ma ọ bụ ihe dakọtara ma ọ bụrụ na ha nwere otu etiti na otu radius. N'ime mgbakọ na mwepụ, nke a pụtara:
\[
P_1 \equiv P_2 \quad \text{na} \quad r_1 = r_2
\]
N'okwu a, \(d = 0\). Okirikiri abụọ ahụ yiri ibe ha, isi ihe ọ bụla dị n'otu okirikiri bụkwa isi ihe dị na okirikiri nke ọzọ.
2. Anaghị ejikọta ọnụ (nke na-anaghị ekewapụ onwe ya)
A na-ekwu na okirikiri abụọ anaghị ejikọta n'okpuru ọnọdụ abụọ:
– Ọnọdụ Mbụ: Mgbe anya dị n'etiti etiti okirikiri abụọ ahụ (d) karịrị mkpokọta ogologo nke radii ha:
\[
d > r_1 + r_2
\]
– Ọnọdụ nke Abụọ: Mgbe otu okirikiri dị n'ime okirikiri ọzọ na-emetụghị aka ma ọlị. Nke a na-eme ma ọ bụrụ na:
\[
d < |r_1 - r_2| \] N'ọnọdụ abụọ a, enweghị ebe a na-ahụkarị n'etiti okirikiri \(C_1\) na \(C_2\). 3. Tangent Mpụta Gburugburu abụọ na-agbanwe agbanwe ma ọ bụrụ na ha emetụ aka n'otu ebe ma dị n'èzí ibe ha. Nke a na-eme ma ọ bụrụ na anya dị n'etiti etiti okirikiri abụọ ahụ hà nhata mkpokọta nke radii ha:
