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 185851 by Mingma last updated on 28/Jan/23

Commented by Mingma last updated on 28/Jan/23

Diameter in relation to a,b,c ?

Answered by mr W last updated on 28/Jan/23

Commented by mr W last updated on 28/Jan/23

R^2 =(c−R)^2 +(((a+b)/2))^2 ⇒R=(c/2)+(((a+b)^2 )/(8c)) OC=R−r OB=c−R+r BC=((a+b)/2)−a=((b−a)/2) (R−r)^2 =(c−R+r)^2 +(((b−a)/2))^2 ⇒r=R−(c/2)−(((b−a)^2 )/(8c)) ⇒r=(((a+b)^2 )/(8c))−(((b−a)^2 )/(8c))=((ab)/(2c)) ⇒d=2r=((ab)/c) ✓ ⇒d=((3×6)/9)=2

$${R}^{\mathrm{2}} =\left({c}−{R}\right)^{\mathrm{2}} +\left(\frac{{a}+{b}}{\mathrm{2}}\right)^{\mathrm{2}} \\ $$$$\Rightarrow{R}=\frac{{c}}{\mathrm{2}}+\frac{\left({a}+{b}\right)^{\mathrm{2}} }{\mathrm{8}{c}} \\ $$$${OC}={R}−{r} \\ $$$${OB}={c}−{R}+{r} \\ $$$${BC}=\frac{{a}+{b}}{\mathrm{2}}−{a}=\frac{{b}−{a}}{\mathrm{2}} \\ $$$$\left({R}−{r}\right)^{\mathrm{2}} =\left({c}−{R}+{r}\right)^{\mathrm{2}} +\left(\frac{{b}−{a}}{\mathrm{2}}\right)^{\mathrm{2}} \\ $$$$\Rightarrow{r}={R}−\frac{{c}}{\mathrm{2}}−\frac{\left({b}−{a}\right)^{\mathrm{2}} }{\mathrm{8}{c}} \\ $$$$\Rightarrow{r}=\frac{\left({a}+{b}\right)^{\mathrm{2}} }{\mathrm{8}{c}}−\frac{\left({b}−{a}\right)^{\mathrm{2}} }{\mathrm{8}{c}}=\frac{{ab}}{\mathrm{2}{c}} \\ $$$$\Rightarrow{d}=\mathrm{2}{r}=\frac{{ab}}{{c}}\:\checkmark \\ $$$$\Rightarrow{d}=\frac{\mathrm{3}×\mathrm{6}}{\mathrm{9}}=\mathrm{2} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com