Lipotso tsa Mehlala le Puisano ea Li-Circle le Li-Chord
Selikalikoe ke e 'ngoe ea libopeho tsa motheo tsa jeometri tse atisang ho ithutoa lipalo. Khopolo e 'ngoe ea bohlokoa e amanang le liselikalikoe ke chord, e leng mola o hokahanyang lintlha tse peli selikalikoeng ntle le ho feta bohareng. Ho utloisisa liselikalikoe le li-chord ho bohlokoa ho ithuteng jeometri. Sehlooho sena se tla tšohla mehlala e 'maloa ea mathata le lipuisano tse amanang le liselikalikoe le li-chord ho tebisa kutloisiso ea rona ea likhopolo tsena.
Kutloisiso ea Motheo
Selikalikoe
Selikalikoe ke pokello ea lintlha tsohle tse ka har'a sefofane tse hole ka ho lekana le ntlha e fanoeng e bitsoang setsi. Haeba setsi sa selikalikoe e le ntlha ea O 'me radius ea selikalikoe e le r, joale selikalikoe se ka hlalosoa ka equation (x - O_x)² + (y - O_y)² = r² ka sebopeho sa Cartesian.
Khoele ea seqha
Khoele e ka har'a selikalikoe ke mola o hokahanyang lintlha tse peli selikalikoeng. Bolelele ba khoele ha bo itšetlehe feela ka radius ea selikalikoe empa hape bo itšetlehile ka boholo ba sekhutlo se bohareng se shebileng ho sona.
Lipotso tsa Mehlala le Puisano
Potso ea 1:
Potso: Fana ka selikalikoe se nang le radius ea 10 cm le chord AB e bolelele ba 16 cm. Fumana sebaka se sekhutšoanyane ho tloha bohareng ba selikalikoe ho ea chord.
Puisano:
Ho fumana sebaka ho tloha bohareng ba selikalikoe ho ea ho chord, re ka sebelisa foromo e nepahetseng ea khutlotharo e entsoeng pakeng tsa radius, sebaka ho tloha bohareng ho ea ho chord, le halofo ea bolelele ba chord.
A re re ntlha O ke bohareng ba selikalikoe 'me ntlha P ke ntlha e bohareng ba chord AB e otlolohileng ho AB. Kahoo, OP ke sebaka se tlohang bohareng ba selikalikoe O ho ea chord AB.
Ka khutlotharo OAP (khutlotharo e ka letsohong le letona ho P), re ka sebelisa Theorem ea Pythagorean:
OP² + AP² = OA²
Rea tseba hore:
– OA (radius ea selikalikoe) = 10 cm
– AB (bolelele ba khoele ea seqha) = 16 cm, kahoo AP = 16/2 = 8 cm.
Kenya boleng bo tsejoang sebakeng sa equation:
OP² + 8² = 10²
OP² + 64 = 100
OP² = 100 – 64
OP² = 36
OP = √36
OP = 6
Kahoo, sebaka se sekgutshwane ho tloha bohareng ba sedikadikwe ho ya ho chord ke 6 cm.
Potso ea 2:
Potso: Selikalikoe se nang le setsi sa O se na le radius ea 8 cm. Chord AB e etsa sekhutlo se bohareng sa ∠AOB sa 120°. Fumana bolelele ba chord AB.
Puisano:
Ho bala bolelele ba chord e bopang sekhutlo se bohareng (θ), re ka sebelisa foromo:
AB = 2 × r × sin(θ/2)
Di mana:
– r ke radius ea selikalikoe (8 cm potsong ena)
– θ ke sekhutlo se entsweng ke chord bohareng ba sedikadikwe (120° bothateng bona)
Kenya mekhoa e tsebahalang sebakeng sa eona:
AB = 2 × 8 cm × sebe(120°/2)
AB = 16 cm × sin(60°)
AB = 16 cm × (√3 / 2)
AB = 8√3 cm
Kahoo, bolelele ba chord AB ke 8√3 cm.
Potso ea 3:
Potso: Selikalikoe se nang le radius ea 13 cm le chord AB se bohōle ba 5 cm ho tloha bohareng ba selikalikoe. Fumana bolelele ba chord AB.
Puisano:
Tabeng ena, re ka sebelisa khutlotharo e nepahetseng e entsoeng ho fumana bolelele ba khoro. A re re ntlha O e be bohareng ba selikalikoe, ntlha P e be ntlha ho khoro e haufi le bohareng, 'me AB e be khoro.
Rea tseba:
– OA (radius ea selikalikoe) = 13 cm
– OP (sebaka se bohareng ho isa khoeleng) = 5 cm.
Ka khutlotharo ea OAP:
OP² + AP² = OA²
Re fumana AP (halofo ea bolelele ba chord):
5² + AP² = 13²
25 + AP² = 169
AP² = 169 – 25
AP² = 144
AP = √144
AP = 12
Kahoo, bolelele ba chord AB = 2 × AP = 2 × 12 = 24 cm.
Potso ea 4:
Potso: Fanoa ka selikalikoe se nang le radius ea 10 cm. Chord AB e na le bolelele ba 12 cm. Fumana boholo ba sekhutlo se bohareng ∠AOB.
Puisano:
Tabeng ena, re hloka ho sebelisa phetoho ea mosebetsi oa trigonometric ho fumana sekhutlo se bohareng ∠AOB. Ho latela foromo ea bolelele ba chord e kenyeletsang sekhutlo se bohareng θ, re ka ngola foromo bocha ho bala θ:
AB = 2 × r × sin(θ/2)
Moo:
– r ke radius ea selikalikoe (10 cm)
– AB ke bolelele ba khoele ea seqha (12 cm)
Beha equation ho arola sin(θ/2):
12 = 2 × 10 × sebe(θ/2)
12 = 20 × sebe(θ/2)
sebe(θ/2) = 12/20
sebe(θ/2) = 0.6
Fumana boleng ba θ/2:
θ/2 = sebe^(-1)(0.6)
θ/2 = 36.87°
Kahoo,:
θ = 2 × 36.87° = 73.74°
Kahoo, sekhutlo se bohareng ∠AOB ke 73.74°.
Qetello
Ho ithuta di-circle le di-chord ho hloka kutlwisiso ya jiometri ya motheo le trigonometry. Mehlaleng e ka hodimo, re bone mokhoa wa ho sebedisa diforomo le di-theorem tse fapaneng, tse kang Pythagorean Theorem, mesebetsi ya trigonometry, le thepa ya motheo ya di-circle, ho rarolla mathata.
Ka mathata ana a ho itloaetsa, ho tšeptjoa hore kutloisiso e tebileng ea kamano pakeng tsa radius, bolelele ba chord, le sekhutlo se bohareng se hlahang e ka finyelloa. Ho utloisisa mohopolo ona ha ho na thuso feela lipalo tsa sekolo empa hape le lits'ebetsong tsa letsatsi le letsatsi mafapheng a fapaneng a saense le boenjiniere.
