Mafunso ndi Zitsanzo za Ma Circles ndi Ma Chords
Bwalo ndi limodzi mwa mawonekedwe oyambira a geometric omwe nthawi zambiri amaphunziridwa mu masamu. Lingaliro limodzi lofunika kwambiri lokhudzana ndi mabwalo ndi chord, yomwe ndi mzere wolumikiza mfundo ziwiri pa bwalo popanda kudutsa pakati. Kumvetsetsa mabwalo ndi ma chord ndikofunikira pophunzira geometry. Nkhaniyi ikambirana zitsanzo zingapo za mavuto ndi zokambirana zokhudzana ndi mabwalo ndi ma chord kuti timvetsetse bwino mfundo izi.
Kumvetsetsa Koyambira
Mzere wozungulira
Bwalo ndi gulu la mfundo zonse zomwe zili mu ndege zomwe zili kutali kwambiri ndi mfundo inayake yotchedwa pakati. Ngati pakati pa bwalo ndi mfundo O ndipo utali wa bwalo ndi r, ndiye kuti bwaloli likhoza kufotokozedwa ndi equation (x – O_x)² + (y – O_y)² = r² mu mawonekedwe a Cartesian.
Chingwe chopindika
Chord mu bwalo ndi mzere womwe umalumikiza mfundo ziwiri pa bwalo. Kutalika kwa chord sikudalira kokha pa utali wa bwalo komanso kukula kwa ngodya yapakati yomwe ikuyang'anizana nalo.
Mafunso ndi Kukambirana Zitsanzo
Funso 1:
Funso: Perekani bwalo lozungulira la 10 cm ndi chord AB yokhala ndi kutalika kwa 16 cm. Dziwani mtunda waufupi kwambiri kuchokera pakati pa bwalo kupita ku chord.
Kukambirana:
Kuti tipeze mtunda kuchokera pakati pa bwalo kupita ku chord, tingagwiritse ntchito njira yolondola ya katatu yopangidwa pakati pa radius, mtunda kuchokera pakati kupita ku chord, ndi theka la kutalika kwa chord.
Tiyerekeze kuti mfundo O ndi pakati pa bwalo ndipo mfundo P ndi pakati pa chord AB yomwe ili yolunjika ku AB. Chifukwa chake, OP ndi mtunda wochokera pakati pa bwalo O kupita ku chord AB.
Mu kansalu kakang'ono ka OAP (kansalu kakang'ono ka kumanja pa P), tingagwiritse ntchito chiphunzitso cha Pythagorean:
OP² + AP² = OA²
Tikudziwa kuti:
– OA (wozungulira wa bwalo) = 10 cm
– AB (kutalika kwa chingwe cha uta) = 16 cm, kotero AP = 16/2 = 8 cm.
Sinthani mfundo zodziwika bwino mu equation:
OP² + 8² = 10²
OP² + 64 = 100
OP² = 100 – 64
OP² = 36
OP = √36
OP = 6
Kotero, mtunda waufupi kwambiri kuchokera pakati pa bwalo kupita ku chord ndi 6 cm.
Funso 2:
Funso: Bwalo lozungulira pakati pa O lili ndi utali wa masentimita 8. Chord AB imapanga ngodya yapakati ∠AOB ya 120°. Dziwani kutalika kwa chord AB.
Kukambirana:
Kuti tiwerenge kutalika kwa chord yomwe imapanga ngodya yapakati (θ), tingagwiritse ntchito fomula iyi:
AB = 2 × r × sin(θ/2)
Kumene:
– r ndi utali wa bwalo (8 cm mu funso ili)
– θ ndi ngodya yomwe imapangidwa ndi chord pakati pa bwalo (120° mu vutoli)
M'malo mwa mfundo zodziwika bwino:
AB = 2 × 8 cm × tchimo (120°/2)
AB = 16 cm × sin(60°)
AB = 16 cm × (√3 / 2)
AB = 8√3 cm
Kotero, kutalika kwa chord AB ndi 8√3 cm.
Funso 3:
Funso: Bwalo lozungulira la 13 cm ndi chord AB lili pa 5 cm kuchokera pakati pa bwalo. Dziwani kutalika kwa chord AB.
Kukambirana:
Pankhaniyi, tingagwiritse ntchito kansalu kolondola komwe kamapangidwa kuti tipeze kutalika kwa chord. Tiyerekeze kuti mfundo O ndi pakati pa bwalo, mfundo P ndi mfundo yomwe ili pa chord yomwe ili pafupi kwambiri ndi pakati, ndipo AB ndi chord.
Tikudziwa:
– OA (wozungulira wa bwalo) = 13 cm
– OP (mtunda wapakati kupita ku chingwe cha uta) = 5 cm.
Mu katatu ka OAP:
OP² + AP² = OA²
Timapeza AP (theka la kutalika kwa chord):
5² + AP² = 13²
25 + AP² = 169
AP² = 169 – 25
AP² = 144
AP = √144
AP = 12
Kotero, kutalika kwa chord AB = 2 × AP = 2 × 12 = 24 cm.
Funso 4:
Funso: Yoperekedwa bwalo lozungulira la 10 cm. Chord AB ili ndi kutalika kwa 12 cm. Dziwani kukula kwa ngodya yapakati ∠AOB.
Kukambirana:
Pankhaniyi, tifunika kugwiritsa ntchito njira yosinthira ya trigonometric kuti tidziwe ngodya yapakati ∠AOB. Kutengera njira ya kutalika kwa chord yomwe ili ndi ngodya yapakati θ, titha kulembanso njirayo kuti tiwerengere θ:
AB = 2 × r × sin(θ/2)
Kumene:
– r ndi utali wa bwalo (10 cm)
– AB ndi kutalika kwa chingwe cha uta (12 cm)
Konzani equation kuti mulekanitse sin(θ/2):
12 = 2 × 10 × sin(θ/2)
12 = 20 × sin(θ/2)
uchimo(θ/2) = 12/20
uchimo(θ/2) = 0.6
Pezani mtengo wa θ/2:
θ/2 = sin^(-1)(0.6)
θ/2 = 36.87°
Kotero,:
θ = 2 × 36.87° = 73.74°
Kotero, ngodya yapakati ∠AOB ndi 73.74°.
Mapeto
Kuphunzira mabwalo ndi ma chord kumafuna kumvetsetsa za geometry yoyambira ndi trigonometry. Mu zitsanzo zomwe zili pamwambapa, taona momwe mungagwiritsire ntchito ma formula ndi ma theorem osiyanasiyana, monga Pythagorean Theorem, ntchito za trigonometric, ndi makhalidwe oyambira a mabwalo, kuti athetse mavuto.
Kudzera mu mavuto oyeserera awa, tikukhulupirira kuti kumvetsetsa bwino ubale womwe ulipo pakati pa radius, kutalika kwa chord, ndi ngodya yapakati yomwe imachokera ku izi kungapezeke. Kumvetsetsa lingaliro ili ndikothandiza osati kokha m'masamu akusukulu komanso m'magwiritsidwe ntchito a tsiku ndi tsiku m'magawo osiyanasiyana a sayansi ndi uinjiniya.
