Question and Answers Forum

All Questions      Topic List

Mensuration Questions

Previous in All Question      Next in All Question      

Previous in Mensuration      Next in Mensuration      

Question Number 25702 by ajfour last updated on 13/Dec/17

Commented by ajfour last updated on 13/Dec/17

solution to Q. 25700

$${solution}\:{to}\:{Q}.\:\mathrm{25700} \\ $$

Answered by ajfour last updated on 13/Dec/17

2x=1cm x+y+z =2cm ...(i) cot θ=((y+z)/R) , and ..(ii) sin θ =((R−r)/(R+r)) =(x/(x+y+z)) ...(iii) ⇒sin θ= ((R−r)/(R+r))=(1/4) or 5r=3R ⇒ cot θ =(√(15)) considering (ii): (√(15)) =(3/(2R)) ⇒ R= (3/(2(√(15)))) =((√(15))/(10)) . r=(3/5)×((√(15))/(10)) =((3(√(15)))/(50)) .

$$\mathrm{2}{x}=\mathrm{1}{cm} \\ $$$${x}+{y}+{z}\:=\mathrm{2}{cm}\:\:\:\:\:\:\:...\left({i}\right) \\ $$$$\mathrm{cot}\:\theta=\frac{{y}+{z}}{{R}}\:\:,\:{and}\:..\left({ii}\right) \\ $$$$\mathrm{sin}\:\theta\:=\frac{{R}−{r}}{{R}+{r}}\:=\frac{{x}}{{x}+{y}+{z}}\:\:\:\:\:\:\:...\left({iii}\right) \\ $$$$\Rightarrow\mathrm{sin}\:\theta=\:\frac{{R}−{r}}{{R}+{r}}=\frac{\mathrm{1}}{\mathrm{4}}\:\:{or}\:\:\:\mathrm{5}{r}=\mathrm{3}{R}\:\:\: \\ $$$$\Rightarrow\:\mathrm{cot}\:\theta\:=\sqrt{\mathrm{15}}\: \\ $$$${considering}\:\left({ii}\right): \\ $$$$\:\:\:\sqrt{\mathrm{15}}\:=\frac{\mathrm{3}}{\mathrm{2}{R}}\:\:\Rightarrow\:{R}=\:\frac{\mathrm{3}}{\mathrm{2}\sqrt{\mathrm{15}}}\:=\frac{\sqrt{\mathrm{15}}}{\mathrm{10}}\:. \\ $$$$\:\:\:\:{r}=\frac{\mathrm{3}}{\mathrm{5}}×\frac{\sqrt{\mathrm{15}}}{\mathrm{10}}\:=\frac{\mathrm{3}\sqrt{\mathrm{15}}}{\mathrm{50}}\:. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com