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Question Number 173273 by mr W last updated on 09/Jul/22

Commented by mr W last updated on 09/Jul/22

$$findthemaximumareaofgreen$$$$inscribedcircle=?$$

Answered by mr W last updated on 09/Jul/22

Commented by mr W last updated on 09/Jul/22

$$AM=\sqrt{{10}^2+5^2}=5\sqrt{5}$$$$r=radiusofgreencircle$$$$SM=5-2r$$$$AN=10-2r$$$$AM=10-2r+2r+5-2r$$$$5\sqrt{5}=15-2r$$$$\Rightarrow r=\frac{5(3-\sqrt{5})}{2}$$$$A_{green}=\pi r^2=\frac{25(7-3\sqrt{5})\pi }{2}$$

Commented by Tawa11 last updated on 11/Jul/22

$$\mathrm{Great}\mathrm{sir}$$

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