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Question Number 209980 by a.lgnaoui last updated on 27/Jul/24

$$\mathrm{determiner}\mathrm{h}?$$$$\mathbf{CD}=20\mathbf{AB}=30$$$$\mathbf{h}1=25$$$$$$

Commented by a.lgnaoui last updated on 27/Jul/24

Commented by mr W last updated on 27/Jul/24

$$is\stackrel{⌢}{CD}semi-circle?$$$$is\stackrel{⌢}{AB}circulararc?$$

Commented by mr W last updated on 27/Jul/24

$$r=radiusof\stackrel{⌢}{CD}$$$$R=radiusof\stackrel{⌢}{AB}$$$$r=\frac{CD}{2}=\frac{20}{2}=10$$$$2R{\sin }^{-1}\frac{15}{R}=\pi r$$$$R{\sin }^{-1}\frac{15}{R}=5\pi \Rightarrow R=30$$$$h=10-(30-\sqrt{{30}^2-{15}^2})=15\sqrt{3}-20\approx 5.98$$

Commented by a.lgnaoui last updated on 28/Jul/24

$$\mathbf{Please},\mathbf{What}\mathbf{will}\mathbf{be}\mathbf{the}\mathbf{value}\mathbf{of}\mathbf{h}\mathbf{if}\mathbf{lignes}\mathbf{AB}\mathbf{and}\mathbf{CD}$$$$\mathbf{are}\mathbf{hyperboliques}?$$

Commented by a.lgnaoui last updated on 28/Jul/24

$$\mathrm{thank}\mathrm{you}$$

Commented by mr W last updated on 28/Jul/24

$$ifthecurvesareparabolasor$$$$hyperbolasthereisnosolution$$$$possible.$$

Commented by Frix last updated on 28/Jul/24

$$2\mathrm{similar}\mathrm{ellipses}\mathrm{are}\mathrm{possible}.$$$$\Rightarrow \stackrel{⌢}{AB}=\stackrel{⌢}{CD}\mathrm{and}\mathrm{we}\mathrm{have}$$$$h_2=h_1-\frac{\mid AB\mid }{2}=10$$$$h=h_1-\frac{\mid CD\mid }{2}=15$$

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