Mehlala ea Lipotso tse Buisanang ka Tlhaloso ea Selikalikoe
Selikalikoe ke e 'ngoe ea libopeho tsa motheo tsa jeometri tseo re kopanang le tsona khafetsa bophelong ba letsatsi le letsatsi. Lipalong, lilikalikoe li na le litlhaloso le litšobotsi tse ikhethang. Sehlooho sena se tla hlahloba tlhaloso ea selikalikoe le likarolo tse amanang le sona ka botebo, hammoho le ho fana ka mehlala e 'maloa ea mathata le litharollo tsa ona ho tebisa kutloisiso ea rona ea lilikalikoe.
Tlhaloso ea Selikalikoe
Selikalikoe ke sete sa lintlha tsohle tse ka har'a sefofane tse hole ka ho lekana le ntlha e tsitsitseng e bitsoang setsi sa selikalikoe. Sebaka se pakeng tsa setsi le ntlha efe kapa efe selikalikoe se bitsoa radius ea selikalikoe. Tekanyo e akaretsang ea selikalikoe se nang le setsi ntlheng \((h, k)\) le radius \(r\) e fanoa ke:
\[ (x – h)^2 + (y – k)^2 = r^2 \]
Mono:
– \((h, k)\) ke dikhokahano tsa bohareng ba sedikadikwe,
– \(r\) ke radius ya sedikadikwe,
– \(x\) le \(y\) ke dikhokahano tsa ntlha efe kapa efe hodima sedikadikwe.
Likarolo tsa Selikalikoe
Pele re kena lipotsong tsa mohlala, ke mohopolo o motle ho tseba tse ling tsa lintlha tsa bohlokoa tse selikalikoeng:
1. Bohareng ba Selikalikoe: Ntlha e tsitsitseng e leng bohareng ba lintlha tsohle tse arohaneng ka sebaka se le seng.
2. Radius (r): Sebaka ho tloha bohareng ba selikalikoe ho ea ntlheng efe kapa efe selikalikoeng.
3. Bophara (d): Mola o otlolohileng o fetang bohareng ba selikalikoe mme o hokahanya dintlha tse pedi selikalikoeng, o na le bolelele bo fetang radius habeli (\(d = 2r\)).
4. Arc: Karolo ea selikalikoe sa selikalikoe e pakeng tsa lintlha tse peli selikalikoeng.
5. Khoro: Mola o otlolohileng o hokahanyang lintlha tse peli selikalikoeng empa o sa fete bohareng.
6. Apothem: Sebaka se sekgutshwane ho tloha bohareng ba sedikadikwe ho ya ho chord.
7. Sekhutlo se Bohareng: Sekhutlo se bopilweng ke di-radii tse pedi ho tloha bohareng ba sedikadikwe.
8. Sekhutlo sa potoloho: Sekhutlo se bopilweng ke di-chord tse pedi tse kopanang ntlheng e le nngwe hodima sedikadikwe.
Lipotso le Lipuisano tsa Mehlala
Mohlala oa Potso ea 1
Potso: Fanoa ka selikalikoe se nang le bohareng ntlheng \((3, 4)\) le ho feta ntlheng \((7, 4)\). Fumana equation ea selikalikoe.
Puisano:
Ho fumana equation ea selikalikoe, re hloka ho tseba radius ea sona pele. Kaha selikalikoe se feta ntlheng \((7, 4)\), re ka bala sebaka se pakeng tsa ntlha ena le bohareng ba selikalikoe, e leng \((3, 4)\).
\[
r = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
\]
\[
r = \ sqrt{(7 – 3)^2 + (4 – 4)^2}
\]
\[
r = \sqrt{4^2 + 0^2}
\]
\[
r = 4
\]
Ka setsi ho \((3, 4)\) le radius 4, equation ea selikalikoe ke:
\[
(x – 3)^2 + (y – 4)^2 = 4^2
\]
\[
(x – 3)^2 + (y – 4)^2 = 16
\]
Mohlala oa Potso ea 2
Potso: Fumana sebaka le selikalikoe sa selikalikoe se nang le radius ea 5 cm.
Puisano:
– Sebaka sa selikalikoe (A) se ka baloa ho sebelisoa foromo \(A = \pi r^2\),
\[
A = \pi \ makhetlo a 5^2
\]
\[
A = 25\pi \text{cm}^2
\]
Haeba \(\pi \approx 3.14\), joale:
\[
A \hoo e ka bang 25 \makhetlo a 3.14 = 78.5 \mongolo{cm}^2
\]
– Selikalikoe sa selikalikoe (C) se ka baloa ho sebelisoa foromo \(C = 2\pi r\),
\[
C = 2 \makgetlo \pi \makgetlo a 5
\]
\[
C = 10\pi \mongolo{cm}
\]
Haeba \(\pi \approx 3.14\), joale:
\[
C \hoo e ka bang 10 \makhetlo a 3.14 = 31.4 \mongolo{cm}
\]
Mohlala oa Potso ea 3
Potso: Selikalikoe se na le setsi ntlheng ea O le radius ea 7 cm. Haeba ho huloa khoele ea bolelele ba 10 cm selikalikoeng, fumana sebaka se sekhutšoanyane ho tloha bohareng ba O ho ea khoeleng.
Puisano:
Ho fumana sebaka se sekgutshwane ho tloha bohareng ho ya ho chord, re sebedisa mohopolo wa apothem, e leng sebaka se sekgutshwane ho tloha bohareng ho ya ho chord. Ka radius ya 7 cm le bolelele ba chord ya 10 cm, re ka atamela bothata bona re sebedisa kgutlotharo e nepahetseng e bopilweng.
Haeba ntlha e bohareng ea chord e le ntlha ea C, joale OC ke apothem eo re e batlang. Haeba A le B e le lipheletso tsa chord, joale AC le BC ka 'ngoe li 5 cm (halofo ea 10 cm).
Ho tloha ho khutlotharo ea OAC e sekametseng ka ho le letona ho C, re sebelisa khopolo-taba ea Pythagorean:
\[
OA^2 = OC^2 + AC^2
\]
\[
7^2 = OC^2 + 5^2
\]
\[
49 = OC^2 + 25
\]
\[
OC^2 = 49 – 25
\]
\[
OC^2 = 24
\]
\[
OC = \sqrt{24} = 2\sqrt{6} \mongolo{cm}
\]
Mohlala oa Potso ea 4
Potso: Fanoe ka selikalikoe se nang le equation \(x^2 + y^2 + 6x – 8y + 9 = 0\). Fumana setsi le radius ea selikalikoe.
Puisano:
Ho fumana setsi le radius, re fetola equation hore e be sebopeho se tloaelehileng:
\[
x^2 + y^2 + 6x – 8y + 9 = 0
\]
Re rarolla bothata ka ho ntlafatsa sebopeho sa quadratic:
\[
x^2 + 6x + y^2 – 8y = -9
\]
Ho eketsa le ho tlosa (6/2)\(^2\) ho x-term le (8/2)\(^2\) ho y-term:
\[
x^2 + 6x + 9 + y^2 – 8y + 16 = -9 + 9 + 16
\]
\[
(x + 3)^2 + (y – 4)^2 = 16
\]
Ho tsoa ho equation \((x + 3)^2 + (y – 4)^2 = 16\), re fumana hore setsi sa selikalikoe ke \((-3, 4)\) mme radius ke \(r = \sqrt{16} = 4\).
Qetello
Selikalikoe ke mohopolo oa motheo le oa bohlokoa thutong ea jeometri. Ka mehlala ea mathata le lipuisano tse kaholimo, re ka fumana kutloisiso e tebileng ea likarolo le litšobotsi tse fapaneng tsa liselikalikoe. Ho tseba sehlooho sena ho tla etsa hore ho be bonolo ho utloisisa le ho rarolla mathata a rarahaneng a jeometri.
