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Category: Geometry

Question-187549

Question Number 187549 by Rupesh123 last updated on 18/Feb/23 Answered by HeferH last updated on 18/Feb/23 $${The}\:{height}\:{of}\:\bigtriangleup{BIC}\:{is}\:{the}\:{inradius}. \\ $$$${Area}\:=\:{s}\centerdot{I} \\ $$$$\:\frac{\sqrt{{s}\left({s}−{a}\right)\left({s}−{b}\right)\left({s}−{c}\right)}}{{s}}\:=\:{I} \\ $$$$\:{s}\:=\:\frac{\mathrm{7}+\mathrm{9}+\mathrm{12}}{\mathrm{2}}\:=\:\mathrm{14} \\ $$$$\:{I}\:=\:\sqrt{\frac{\left(\mathrm{14}−\mathrm{9}\right)\left(\mathrm{14}−\mathrm{7}\right)\left(\mathrm{14}−\mathrm{12}\right)}{\mathrm{14}}}\:=\:\sqrt{\mathrm{5}}…

n-1-1-n-4n-2n-

Question Number 121985 by Dwaipayan Shikari last updated on 13/Nov/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}\begin{pmatrix}{\mathrm{4n}}\\{\mathrm{2n}}\end{pmatrix}} \\ $$ Commented by Dwaipayan Shikari last updated on 13/Nov/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty}…

Question-187482

Question Number 187482 by ajfour last updated on 17/Feb/23 Commented by ajfour last updated on 17/Feb/23 $${If}\:\:\:\:{cone}'{s}\:\:\:\:\:\frac{{R}}{{h}}={m},\:\:{green}\:{ball} \\ $$$${radius}={a}.\:\:{Find}\:{b}\:{the}\:{radii}\:{of} \\ $$$${upper}\:{balls}\:\left({equal}\right),\:{all}\:{in}\:{contact} \\ $$$${the}\:{way}\:{shown}. \\ $$…

Question-187452

Question Number 187452 by Rupesh123 last updated on 17/Feb/23 Answered by mr W last updated on 17/Feb/23 $${side}\:{length}\:{of}\:{octagon}\:=\:{a} \\ $$$${area}\:{of}\:{octagon}\:{A}_{\mathrm{8}} =\left({a}+\mathrm{2}×\frac{{a}}{\:\sqrt{\mathrm{2}}}\right)^{\mathrm{2}} −{a}^{\mathrm{2}} =\mathrm{2}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right){a}^{\mathrm{2}} \\ $$$${black}\:{area}\:{A}_{{black}}…