Question Number 128944 by ajfour last updated on 11/Jan/21 Commented by ajfour last updated on 11/Jan/21 $${Find}\:{radius}\:{ratio}\:\frac{{R}}{{r}}. \\ $$$${The}\:{polygon}\:{is}\:{a}\:{regular} \\ $$$${pentagon}. \\ $$ Answered by…
Question Number 63324 by pradyot_pathak last updated on 02/Jul/19 Answered by Hope last updated on 02/Jul/19 $${area}\:{of}\:{pentagon}=\frac{\mathrm{1}}{\mathrm{4}}×\mathrm{5}×\mathrm{12}^{\mathrm{2}} ×{cot}\left(\frac{\mathrm{180}^{{o}} }{\mathrm{5}}\right) \\ $$$$=\mathrm{180}×{cot}\mathrm{36}^{{o}} \\ $$$${external}\:{angle}=\frac{\mathrm{360}^{{o}} }{\mathrm{5}}=\mathrm{72}^{{o}} \\…
Question Number 128805 by bramlexs22 last updated on 10/Jan/21 $$\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{e}^{\mathrm{i}\theta} +\mathrm{1}\:=\:\mathrm{e}^{−\frac{\mathrm{i}\theta}{\mathrm{2}}} \:+\:\mathrm{e}^{\frac{\mathrm{i}\theta}{\mathrm{2}}} \:? \\ $$ Commented by mr W last updated on 10/Jan/21 $${LHS}=\left(\mathrm{1}+\mathrm{cos}\:\theta\right)+{i}\:\mathrm{sin}\:\theta \\…
Question Number 63233 by lalitchand last updated on 01/Jul/19 Commented by lalitchand last updated on 01/Jul/19 $$\mathrm{question}\:\mathrm{nmbr}\:\mathrm{10} \\ $$ Commented by arcana last updated on…
Question Number 128764 by behi83417@gmail.com last updated on 10/Jan/21 Commented by behi83417@gmail.com last updated on 10/Jan/21 $$\measuredangle\mathrm{DAB}=\measuredangle\mathrm{CBA}=\mathrm{30}^{\bullet} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{AB}}=? \\ $$ Answered by Olaf last…
Question Number 63206 by lalitchand last updated on 30/Jun/19 Commented by lalitchand last updated on 30/Jun/19 $$\mathrm{question}\:\mathrm{number}\:\mathrm{8} \\ $$ Answered by arcana last updated on…
Question Number 63203 by lalitchand last updated on 30/Jun/19 Commented by lalitchand last updated on 30/Jun/19 $$\mathrm{question}\:\mathrm{number}\:\mathrm{6} \\ $$ Commented by arcana last updated on…
Question Number 63194 by lalitchand last updated on 30/Jun/19 Answered by mr W last updated on 30/Jun/19 $$\frac{\Delta{AQR}}{\Delta{ABC}}=\left(\frac{{AQ}}{{AB}}\right)^{\mathrm{2}} =\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{2}} =\frac{\mathrm{4}}{\mathrm{9}} \\ $$$$\frac{\Delta{APS}}{\Delta{ABC}}=\left(\frac{{AP}}{{AB}}\right)^{\mathrm{2}} =\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{9}} \\…
Question Number 63176 by ajfour last updated on 30/Jun/19 Commented by ajfour last updated on 30/Jun/19 $${Find}\:{maximum}\:{coloured}\:{area} \\ $$$${if}\:{line}\:{segments}\:{BP}\:{and}\:{AP}\: \\ $$$${lie}\:{entirely}\:{outside}\:{the}\:{circle}. \\ $$ Answered by…
Question Number 128652 by ajfour last updated on 09/Jan/21 Commented by ajfour last updated on 09/Jan/21 $${Find}\:{the}\:{radius}\:{of}\:{outer}\:{circle} \\ $$$${in}\:{terms}\:{of}\:{inradii}\:{R}\:{and}\:{r}\:{of} \\ $$$${two}\:{isosceles}\:{right}\:{angled}\: \\ $$$${triangles}\:\left({as}\:{shown},\:{see}\:{fig}\right). \\ $$…