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Question Number 157225 by mr W last updated on 21/Oct/21

Commented by mr W last updated on 21/Oct/21

$$SolutiontoQ157114$$$$$$$$AD=\sqrt{{15}^2-{\left(3x\right)}^2}$$$$AO=\frac{3}{2}AD=\frac{3\sqrt{225-9x^2}}{2}$$$$FO=\sqrt{{\left(8x\right)}^2+{AO}^2}=\sqrt{64x^2+\frac{9(225-9x^2)}{4}}$$$$=\frac{1}{2}\sqrt{175x^2+2025}$$$$CF=\frac{2}{5}FO=\frac{1}{5}\sqrt{175x^2+2025}$$$$CO=\frac{3}{5}FO=\frac{3}{10}\sqrt{175x^2+2025}$$$$\frac{{AC}^2+{CO}^2-{AO}^2}{2\times AC\times CO}=\frac{{AF}^2-{AC}^2-{CF}^2}{2\times AC\times CF}$$$$\frac{36\times 5+\frac{9(175x^2+2025)}{100}-\frac{9(225-9x^2)}{4}}{\frac{3}{10}\sqrt{175x^2+2025}}=\frac{64x^2-36\times 5-\frac{175x^2+2025}{25}}{\frac{1}{5}\sqrt{175x^2+2025}}$$$$x^2=5$$$$x=\sqrt{5}$$$$?=AF=8x=8\sqrt{5}$$

Commented by Tawa11 last updated on 21/Oct/21

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

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