Ajụjụ Ihe Nlereanya Na-atụle Ọnọdụ nke Gburugburu Abụọ
Pendahuluan
Okirikiri ahụ bụ otu n'ime ọdịdị dị mkpa na geometry nke anyị na-ahụkarị n'ọtụtụ nsogbu mgbakọ na mwepụ. Ịmụ ọnọdụ okirikiri abụọ bụ isiokwu dị mkpa n'ihi ọtụtụ ojiji ya na ndụ kwa ụbọchị. Na mgbakọ na mwepụ, enwere ike inyocha ọnọdụ okirikiri abụọ site na inyocha ọnọdụ ha dabere na anya dị n'etiti etiti ha na radii ha.
Echiche nke Ọnọdụ nke Gburugburu Abụọ
Iji chọpụta ọnọdụ okirikiri abụọ, anyị na-eji ọtụtụ paramita bụ isi:
1. Radius nke okirikiri mbụ (r1)
2. radius nke okirikiri nke abụọ (r2)
3. Anya dị n'etiti etiti okirikiri abụọ ahụ (d)
Dabere na ụkpụrụ ndị a, enwere ọtụtụ ọnọdụ nwere ike ịbụ nke okirikiri abụọ ahụ:
1. Gburugburu ahụ dị ka tangent site n'èzí
– Ọ na-eme ma ọ bụrụ na d = r1 + r2.
2. Okirikiri na-ejikọta ọnụ site n'ime
– Ọ na-eme ma ọ bụrụ na d = |r1 – r2|.
3. Okirikiri ndị na-ekewapụ
– Na-eme ma ọ bụrụ |r1 – r2| < d < r1 + r2. 4. Okirikiri na-ekewapụ - Na-eme ma ọ bụrụ d > r1 + r2.
5. Otu okirikiri n'ime okirikiri ọzọ na-emetụghị aka
– Na-eme ma ọ bụrụ na d < |r1 - r2|. 6. Okirikiri na-ejikọta otu kpọmkwem n'ime nke ọzọ – Na-eme ma ọ bụrụ na d = 0 na r1 = r2 (ha abụọ bụ otu okirikiri). Ajụjụ na Mkparịta ụka Ihe atụ Ka anyị lelee ụfọdụ ajụjụ ihe atụ iji ghọta nke ọma ọnọdụ okirikiri abụọ. Ihe atụ Ajụjụ nke 1: Okirikiri Na-ekewapụ n'èzí Ajụjụ: E nyere okirikiri abụọ nwere etiti na isi ihe A na B, anya AB dịkwa 10 cm. Okirikiri nke okirikiri mbụ bụ 6 cm, ebe okirikiri nke okirikiri nke abụọ bụ 4 cm. Chọpụta ọnọdụ okirikiri abụọ ahụ. Mkparịta ụka: - E nyere: - radius nke okirikiri mbụ, r1 = 6 cm - radius nke okirikiri nke abụọ, r2 = 4 cm - Anya dị n'etiti etiti okirikiri, d = 10 cm Maka ọnọdụ tangent mpụga: \[ d = r1 + r2 \] Tinye ụkpụrụ ndị a: \[ d = 6 + 4 \] \[ d = 10 \] Ebe ọ bụ na d = 10 cm, nke hà nhata ngụkọta nke r1 na r2, okirikiri abụọ ahụ bụ tangent mpụga. Ihe atụ Ajụjụ nke 2: Gburugburu Tangent dị n'ime Ajụjụ: Gburugburu abụọ nwere radius nke 8 cm na 3 cm n'otu n'otu nwere anya dị n'etiti etiti nke 5 cm. Chọpụta ọnọdụ okirikiri abụọ ahụ. Mkparịta ụka: - E nyere: - radius nke okirikiri mbụ, r1 = 8 cm - radius nke okirikiri nke abụọ, r2 = 3 cm - Anya dị n'etiti etiti okirikiri, d = 5 cm Maka ọnọdụ tangent dị n'ime: \[ d = |r1 - r2| \] Gbakọọ: \[ d = |8 - 3| \] \[ d = 5 \] Ebe ọ bụ na d = 5 cm, nke hà nhata na ọdịiche nke r1 na r2, okirikiri abụọ ahụ na-ejikọ n'ime. Ihe atụ Ajụjụ nke 3: Gburugburu Ndị Na-ekewa Ajụjụ: Gburugburu abụọ nwere radii nke 7 cm na 5 cm n'otu n'otu yana anya dị n'etiti etiti ha nke 9 cm. Chọpụta ọnọdụ okirikiri abụọ ahụ. Mkparịta ụka: - E nyere: - Radius nke okirikiri mbụ, r1 = 7 cm - Radius nke okirikiri nke abụọ, r2 = 5 cm - Anya dị n'etiti etiti okirikiri, d = 9 cm Maka ọnọdụ njikọta: \[ |r1 - r2| < d < r1 + r2 \] Gbakọọ: \[ |7 - 5| < 9 < 7 + 5 \] \[ 2 < 9 < 12 \] Ebe ọ bụ na uru nke d dara n'etiti |r1 - r2| na r1 + r2, mgbe ahụ okirikiri abụọ ahụ na-ejikọ. Ihe atụ Ajụjụ nke 4: Gburugburu Ndị Na-ekewapụ Onwe Ha Ajụjụ: Gburugburu nwere radii nke 2 cm na 3 cm nwere anya n'etiti etiti ha nke 7 cm. Chọpụta ọnọdụ okirikiri abụọ ahụ. Mkparịta ụka: - Enyere: - radius nke okirikiri mbụ, r1 = 2 cm - radius nke okirikiri nke abụọ, r2 = 3 cm - Anya dị n'etiti etiti okirikiri, d = 7 cm Maka ọnọdụ ndị na-ekewapụ onwe ha: \[ d > r1 + r2 \]
Ọnụọgụ:
\[ 7 > 2 + 3 \]
\[ 7 > 5 \]
Ebe ọ bụ na d karịrị ngụkọta nke r1 na r2, a na-ekewapụ okirikiri abụọ ahụ site n'otu ebe.
Ihe atụ Ajụjụ nke 5: Otu okirikiri n'ime nke ọzọ na-emetụghị aka
Ajụjụ:
Okirikiri abụọ nwere radii nke 8 cm na 2 cm n'otu n'otu nwere anya dị n'etiti etiti ha nke 5 cm. Chọpụta ebe okirikiri abụọ ahụ dị.
Azịza:
- A maara:
– Oke okirikiri nke okirikiri mbụ, r1 = 8 cm
– Oke okirikiri nke okirikiri nke abụọ, r2 = 2 cm
– Ogologo dị n'etiti etiti okirikiri ahụ, d = 5 cm
Maka ọnọdụ nke otu n'ime ibe ya na-emetụghị aka:
\[ d < |r1 - r2| \] Gbakọọ: \[ d < |8 - 2| \] \[ 5 < 6 \] Ebe ọ bụ na d pere mpe karịa ọdịiche dị n'etiti r1 na r2, otu okirikiri dị n'ime nke ọzọ na-emetụghị aka. Mmechi Ịghọta ọnọdụ nke okirikiri abụọ nwere ike inyere anyị aka n'ọtụtụ ojiji nke geometry na omume ụwa n'ezie. Site n'ịmata mmekọrịta dị n'etiti radius nke okirikiri na anya dị n'etiti etiti ya, anyị nwere ike ikpebi ma okirikiri abụọ ahụ metụrụ aka n'èzí ma ọ bụ n'ime, ma ọ bụ na-ejikọta ọnụ, ma ọ bụ na ha adịghị n'otu. Site na ihe atụ ndị dị n'elu, a na-atụ anya na ndị na-agụ akwụkwọ ga-aghọta echiche a nke ọma ma tinye ya n'ọrụ n'ọnọdụ mgbakọ na mwepụ dị iche iche. Gaa n'ihu na-eme ihe gbasara nsogbu dị iche iche iji mee ka nkà nyocha gị na nghọta nke ọnọdụ nke okirikiri abụọ dịkwuo mma. Ka ị na-emekwu ihe, otú ahụ ka ọ ga-adịrị anyị mfe idozi nsogbu dị iche iche metụtara okirikiri na geometry.
