Ajụjụ Ihe Nlereanya Na-atụle Nkọwa nke Gburugburu
Okirikiri ahụ bụ otu n'ime ọdịdị geometric bụ isi anyị na-ezutekarị na ndụ kwa ụbọchị. Na mgbakọ na mwepụ, okirikiri nwere nkọwa na njirimara pụrụ iche. Isiokwu a ga-enyocha nkọwa nke okirikiri na ihe ndị metụtara ya nke ọma, yana inye ọtụtụ ihe atụ nsogbu na ngwọta ha iji mee ka nghọta anyị banyere okirikiri dịkwuo omimi.
Nkọwa nke okirikiri
Okirikiri bụ otu isi ihe niile dị n'ụgbọelu nke dị anya site na ebe a kapịrị ọnụ nke a na-akpọ etiti okirikiri ahụ. A na-akpọ anya dị n'etiti etiti na isi ihe ọ bụla dị na okirikiri ahụ radius nke okirikiri ahụ. Enyere nha nhata izugbe nke okirikiri nwere etiti na isi \((h, k)\) na radius \(r\) site na:
\[ (x – h)^2 + (y – k)^2 = r^2 \]
Ebe ahụ:
– \((h, k)\) bụ nhazi nke etiti okirikiri ahụ,
– \(r\) bụ radius nke okirikiri ahụ,
– \(x\) na \(y\) bụ nhazi nke isi ihe ọ bụla dị na okirikiri ahụ.
Ihe Ndị Dị n'Okirikiri
Tupu anyị abanye n'ajụjụ ndị a, ọ dị mma ịmara ụfọdụ ihe dị mkpa dị na okirikiri ahụ:
1. Ebe etiti okirikiri: Ebe a kapịrị ọnụ nke bụ etiti isi ihe niile dị otu anya.
2. Radius (r): Anya site n'etiti okirikiri ahụ ruo ebe ọ bụla dị na okirikiri ahụ.
3. Dayameta (d): Ahịrị kwụ ọtọ nke gafere etiti okirikiri ahụ ma jikọta isi ihe abụọ dị na okirikiri ahụ, nwere ogologo okpukpu abụọ nke radius (\(d = 2r\)).
4. Arc: Akụkụ nke gburugburu nke okirikiri nke dị n'etiti isi ihe abụọ dị na okirikiri ahụ.
5. Kọọd: Ahịrị kwụ ọtọ nke na-ejikọta isi ihe abụọ na okirikiri mana ọ naghị agafe n'etiti.
6. Apothem: Anya kacha nso site n'etiti okirikiri ruo na kọd.
7. Etiti Akuku: E ji radii abụọ sitere n'etiti okirikiri ahụ mepụta akụkụ ahụ.
8. Akụkụ Perimeta: Akụkụ nke a na-eji kọd abụọ na-ejikọta n'otu ebe na okirikiri.
Ajụjụ na Mkparịta ụka Ndị Dị Mkpa
Ajụjụ Ihe Nlereanya nke 1
Ajụjụ: E nyere okirikiri nwere etiti na isi \(3, 4)\) na ịgafe isi \(7, 4)\). Chọpụta nha nhata nke okirikiri ahụ.
Mkparịta ụka:
Iji chọta nha nhata nke okirikiri, anyị kwesịrị ibu ụzọ mara radius ya. Ebe ọ bụ na okirikiri ahụ gafere isi ihe \(7, 4)\, anyị nwere ike ịgbakọ anya dị n'etiti isi ihe a na etiti okirikiri ahụ, nke bụ \((3, 4)\).
\[
r = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
\]
\[
r = \sqrt{(7 – 3)^2 + (4 – 4)^2}
\]
\[
r = \sqrt{4^2 + 0^2}
\]
\[
r = 4
\]
Site na etiti dị na \(3, 4)\) na radius 4, nha nha nke okirikiri ahụ bụ:
\[
(x – 3)^2 + (y – 4)^2 = 4^2
\]
\[
(x – 3)^2 + (y – 4)^2 = 16
\]
Ajụjụ Ihe Nlereanya nke 2
Ajụjụ: Chọpụta ebe na gburugburu nke okirikiri nwere radius nke 5 cm.
Mkparịta ụka:
– Enwere ike ịgbakọ mpaghara okirikiri (A) site na iji usoro \(A = \pi r^2\),
\[
A = \pi \ugboro 5^2
\]
\[
A = 25\pi \ederede{ cm}^2
\]
Ọ bụrụ na \(\pi \ihe dịka 3.14\), mgbe ahụ:
\[
A \ihe dị ka ugboro 25 3.14 = 78.5 \ederede{ cm}^2
\]
– Enwere ike ịgbakọ okirikiri nke okirikiri (C) site na iji usoro \(C = 2\pi r\),
\[
C = ugboro abụọ \pi \ ugboro ise
\]
\[
C = 10\pi \ederede{ cm}
\]
Ọ bụrụ na \(\pi \ihe dịka 3.14\), mgbe ahụ:
\[
C \ihe dị ka ugboro iri 3.14 = 31.4 \ederede{ cm}
\]
Ajụjụ Ihe Nlereanya nke 3
Ajụjụ: Okirikiri nwere etiti na isi ihe O na radius nke 7 cm. Ọ bụrụ na a dọwara eriri ogologo nke 10 cm na okirikiri ahụ, chọpụta anya kacha nso site na etiti O ruo na eriri ahụ.
Mkparịta ụka:
Iji chọta anya kacha nso site n'etiti ruo na kọd, anyị na-eji echiche nke apothem, nke bụ anya kacha nso site n'etiti ruo na kọd. Site na radius nke 7 cm na ogologo kọd nke 10 cm, anyị nwere ike ileba anya na nsogbu a site na iji triangle ziri ezi e guzobere.
Ọ bụrụ na etiti nke kọd bụ isi C, mgbe ahụ OC bụ apothem anyị na-achọ. Ọ bụrụ na A na B bụ njedebe nke kọd ahụ, mgbe ahụ AC na BC bụ 5 cm (ọkara nke 10 cm).
Site na triangle OAC nke nwere akụkụ aka nri na C, anyị na-eji usoro Pythagorean:
\[
OA^2 = OC^2 + AC^2
\]
\[
7^2 = OC^2 + 5^2
\]
\[
49 = OC^2 + 25
\]
\[
OC^2 = 49 – 25
\]
\[
OC^2 = 24
\]
\[
OC = \sqrt{24} = 2\sqrt{6} \ederede{ cm}
\]
Ajụjụ Ihe Nlereanya nke 4
Ajụjụ: E nyere okirikiri nwere nha anya \(x^2 + y^2 + 6x – 8y + 9 = 0\). Chọpụta etiti na radius nke okirikiri ahụ.
Mkparịta ụka:
Iji chọta etiti na radius, anyị na-agbanwe nha nhata ka ọ bụrụ ụdị ọkọlọtọ:
\[
x^2 + y^2 + 6x – 8y + 9 = 0
\]
Anyị na-edozi site n'ịmezi ụdị quadratic:
\[
x^2 + 6x + y^2 – 8y = -9
\]
Ịgbakwunye na iwepụ (6/2)\(^2\) na x-term na (8/2)\(^2\) na y-term:
\[
x^2 + 6x + 9 + y^2 – 8y + 16 = -9 + 9 + 16
\]
\[
(x + 3)^2 + (y – 4)^2 = 16
\]
Site na nha anya \((x + 3)^2 + (y – 4)^2 = 16\), anyị na-achọpụta na etiti okirikiri ahụ bụ \((-3, 4)\) na radius ahụ bụ \(r = \sqrt{16} = 4\).
Mmechi
Okirikiri ahụ bụ echiche dị mkpa ma dị mkpa na geometry. Site na nsogbu na mkparịta ụka dị n'elu, anyị nwere ike ịghọta nke ọma akụkụ na ihe onwunwe dị iche iche nke okirikiri. Ịmụta isiokwu a ga-eme ka ọ dịrị mfe nghọta na idozi nsogbu geometry ndị dị mgbagwoju anya karị.
