Yuav ua li cas mus nrhiav tau cov voos kheej-kheej ntawm ib lub voj voog: los pab cov tub ntxhais kawm

Yuav ua li cas mus nrhiav tau cov voos kheej-kheej ntawm lub vajvoog? Lo lus nug no yeej tseem ceeb rau cov tub ntxhais kawm kawm planimetry. Hauv qab no peb saib ib co piv txwv ntawm yuav ua li cas koj yuav puag nrog neeg ua hauj lwm.

Nyob ntawm seb lub voos kheej-kheej ntawm lub vajvoog ua hauj lwm tej yam kev mob, koj muaj peev xwm nrhiav tau ib txoj kev.

Formula 1: R = L / 2π, qhov twg A - yog qhov ib ncig, thiab π - qhov sib npaug zos rau 3.141 ...

Formula 2: R = √ (S / π), qhov chaw uas S - yog tus nqi ntawm cov cheeb tsam ntawm ib lub voj voog.

Formula 3: R = D / 2 qhov twg D - yog lub lub cheeb ntawm lub voj voog, i.e. qhov ntev ntawm lub seem uas, dhau los ntawm qhov chaw ntawm lub daim duab txuas lub ob maximally spaced apart cov ntsiab lus.

Yuav ua li cas mus nrhiav tau cov voos kheej-kheej ntawm lub circumcircle

Thawj peb txhais lub sij hawm nws tus kheej. Circumference hu tau piav thaum nws kev txhawj xeeb rau tag nrho cov polygon vertices. Nws yuav tsum tau muab sau tseg hais tias ib lub voj voog yuav piav ib ncig ntawm tsuas xws li ib tug polygon, uas nws sab thiab cov ces kaum yog muaj sib npaug rau txhua tus lwm yam, uas yog, nyob ib ncig ntawm ib tug equilateral triangle, square, rhombus, thiab lwm yam txoj cai Yuav kom daws tau qhov teeb meem no nws yog tsim nyog los nrhiav tau ntawm lub perimeter ntawm ib tug polygon, thiab tuag tawm ntawm nws txhais tes thiab lub cheeb tsam. Yog li ntawd, armed nrog ib tug kav, compass, tshuab xam zauv, thiab ib phau nrog ib tug cwj mem.

Yuav ua li cas mus nrhiav tau cov voos kheej-kheej ntawm lub vajvoog, yog hais tias nws yog piav txog ib tug daim duab peb sab

Formula 1: R = (A * B * B) / 4S, qhov twg A, B, C, - ntev ntawm daim duab peb sab sab, thiab S - nws cheeb tsam.

Formula 2: R = A / kev txhaum ib, qhov twg A - qhov ntev ntawm ib sab ntawm daim duab, thiab kev txhaum thiab - ib tug xam tus nqi ntawm lub sine ntawm qhov opposite lub sab.

Lub voos kheej-kheej ntawm lub vajvoog piav ib ncig ntawm lub txoj cai-angled daim duab peb sab.

Formula 1: R = B / 2, nyob qhov twg B - hypotenuse.

Formula 2: R = M * B, qhov twg B - hypotenuse, thiab M - theem nrab ua thereto.

Yuav ua li cas mus nrhiav tau cov voos kheej-kheej ntawm ib lub voj voog yog hais tias nws yog piav nyob ib ncig ntawm ib tug tsis tu ncua polygon

Formula: R = A / (2 * kev txhaum (360 / (2 * n))), qhov chaw uas A - qhov ntev ntawm ib sab ntawm daim duab, thiab n - tus naj npawb ntawm sab nyob rau hauv lub geometrical daim duab.

Yuav ua li cas mus nrhiav tau cov voos kheej-kheej ntawm lub incircle

Lub inscribed vajvoog yog hu ua thaum nws siv tau rau tag nrho cov sab ntawm cov duab. Xav txog ob peb yam piv txwv.

Formula 1: R = S / (P / 2) nyob qhov twg - S thiab R - lub cheeb tsam thiab puag ncig ntawm cov duab ntsig txog.

Formula 2: R = (P / 2 - A) * TG (a / 2), qhov chaw uas P - puag ncig A - ntev ntawm ib qho ntawm ob tog, thiab - opposite no sab ntawm lub kaum sab xis.

Yuav ua li cas mus nrhiav tau cov voos kheej-kheej ntawm lub vajvoog, yog hais tias nws yog inscribed nyob rau hauv ib txoj cai daim duab peb sab

Formula 1:

Lub voos kheej-kheej ntawm lub vajvoog uas yog inscribed nyob rau hauv lub rhomb

Ib tug vajvoog yuav inscribed nyob rau hauv tej rhombus yog ib tug equilateral thiab scalene.

Formula 1: R = 2 * H, qhov twg H - rau qhov siab ntawm cov geometric zoo.

Formula 2: R = S / (A * 2), qhov chaw uas S - yog lub cheeb tsam ntawm lub rhombus, thiab A - sab ntawm nws kav ntev npaum.

Formula 3: R = √ ((S * txhaum A) / 4), qhov chaw uas S - yog lub cheeb tsam ntawm lub rhombus, thiab A txhaum - sine mob kaum sab xis ntawm lub geometrical daim duab.

Formula 4: R = V * T / (√ (V² + G²) qhov twg B thiab T - yog qhov ntev ntawm lub diagonals ntawm lub geometrical daim duab.

Formula 5: R = B * kev txhaum (A / 2), nyob qhov twg - lub kab pheeb ces kaum ntawm lub rhombus, thiab A - yog lub kaum sab xis ntawm lub vertices uas txuas lub kab pheeb ces kaum.

Lub voos kheej-kheej ntawm lub vajvoog uas yog inscribed nyob rau hauv daim duab peb sab

Nyob rau hauv cov kev tshwm sim hais tias nyob rau hauv lub teeb meem uas koj muab lub lengths ntawm lub sab ntawm daim duab, thawj xam lub perimeter ntawm lub daim duab peb sab (U), thiab ces ib nrab-puag ncig (n):

P = A + B + C, qhov twg A, B, - tus lengths ntawm sab ntawm lub duab daim duab.

n = n / 2.

Formula 1: R = √ ((p-A) * (n-D) * (n-B) / n).

Thiab yog hais tias, kev paub txog tag nrho cov tib peb ob tog, koj yuav muab ntau thiab cheeb tsam ntawm daim duab, koj yuav xam lub yam ntau yam raws li nram no.

Formula 2: R = S * 2 (A + B + C)

Formula 3: R = S / f = S / (A + B + C) / 2), nyob qhov twg - n - yog semiperimeter geometric duab.

Formula 4: R = (n - k) * TG (A / 2), qhov chaw uas n - yog semiperimeter daim duab peb sab A - ib qho ntawm nws sab, thiab TG (A / 2) - tangent ntawm ib nrab qhov no sab ntawm lub opposite lub.

Ib tug hauv qab no lub saum toj no mis yuav nrhiav tau cov voos kheej-kheej ntawm lub vajvoog uas yog inscribed nyob rau hauv ib tug equilateral daim duab peb sab.

Formula 5: R = A * √3 / 6.

Lub voos kheej-kheej ntawm lub vajvoog uas yog inscribed nyob rau hauv ib txoj cai daim duab peb sab

Yog hais tias ib qho teeb meem muab qhov ntev ntawm ob txhais ceg thiab lub hypotenuse, ces tus voos kheej-kheej ntawm lub inscribed vajvoog raws li yog pom tau hais tias.

Formula 1: R = (A + B-C) / 2, nyob qhov twg A thiab B - ob txhais ceg, C - hypotenuse.

Nyob rau hauv cov ntaub ntawv uas, yog hais tias koj tsuas yog ob tug ceg, nws yog lub sij hawm mus nco txog lub Pythagorean theorem mus nrhiav tus hypotenuse thiab siv cov saum toj no mis.

C = √ (A² + B²).

Lub voos kheej-kheej ntawm lub vajvoog uas yog inscribed nyob rau hauv ib tug square

Vajvoog uas yog inscribed nyob rau hauv ib tug square, faib tag nrho nws cov 4 sab raws nraim ib nrab ntawm cov ntsiab lus ntawm tangency.

Formula 1: R = A / 2, nyob qhov twg A - sab ntev ntawm ib tug square.

Formula 2: R = S / (P / 2), qhov chaw uas S thiab F - lub cheeb tsam thiab puag ncig ntawm ib tug square, ntsig txog.