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Category: Geometry

Question-219723

Question Number 219723 by Spillover last updated on 01/May/25 Answered by mehdee7396 last updated on 03/May/25 $$\:{OB}=\mathrm{4}\Rightarrow{OT}=\mathrm{2}\Rightarrow{r}=\mathrm{3} \\ $$$${BT}=\mathrm{2}\sqrt{\mathrm{3}} \\ $$$${BT}×{AT}={KT}×{TT}' \\ $$$$\mathrm{12}=\mathrm{6}×{TT}'\Rightarrow{TT}'=\mathrm{2}\Rightarrow{r}'=\mathrm{1} \\ $$$${S}=\mathrm{16}\pi−\mathrm{9}\pi−\mathrm{1}\pi=\mathrm{6}\pi…

Question-219425

Question Number 219425 by Nicholas666 last updated on 24/Apr/25 Commented by Nicholas666 last updated on 24/Apr/25 $$\:\:\:\:{ABC}\:{reguler}\:{pentagon}\: \\ $$$$\:\:\:{P},\:{Q},\:{T}\:\:\:\:\:{toricelli}'{s}\:{point}\:{of}\:{AED},{BCD},{ADE}\:\:\:\:\: \\ $$$$\:\:\:{find}\:{angle}\:{PTQ}? \\ $$ Answered by…

Question-219339

Question Number 219339 by Spillover last updated on 23/Apr/25 Answered by mr W last updated on 23/Apr/25 $$\alpha=\mathrm{45}°+\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{tan}\:\alpha=\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{1}−\mathrm{1}×\frac{\mathrm{1}}{\mathrm{2}}}=\mathrm{3} \\ $$ Answered by…