Question Number 226908 by mr W last updated on 18/Dec/25
Commented by mr W last updated on 18/Dec/25
$${find}\:{the}\:{area}\:{of}\:{the}\:{circle}. \\ $$
Answered by A5T last updated on 19/Dec/25
$$\mathrm{Let}\:\mid\mathrm{AB}\mid=\mathrm{4}\:\mathrm{and}\:\mid\mathrm{CD}\mid=\mathrm{2};\:\mathrm{let}\:\mathrm{AD}\cap\mathrm{BC}=\mathrm{E} \\ $$$$\mathrm{Q225840}\:\Rightarrow\:\mathrm{CE}^{\mathrm{2}} +\mathrm{EB}^{\mathrm{2}} +\mathrm{EA}^{\mathrm{2}} +\mathrm{ED}^{\mathrm{2}} =\mathrm{4R}^{\mathrm{2}} \\ $$$$\mathrm{But}\:\mathrm{CE}^{\mathrm{2}} +\mathrm{ED}^{\mathrm{2}} =\mathrm{2}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{EA}^{\mathrm{2}} +\mathrm{EB}^{\mathrm{2}} =\mathrm{4}^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{4R}^{\mathrm{2}} =\mathrm{2}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} =\mathrm{20}\:\Rightarrow\:\mathrm{Area}=\mathrm{5}\pi \\ $$
Commented by mr W last updated on 20/Dec/25
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