Question Number 205734 by mr W last updated on 28/Mar/24
Answered by A5T last updated on 28/Mar/24
Commented by A5T last updated on 28/Mar/24
$$\frac{\mathrm{48}×\mathrm{144}×\mathrm{13}}{\mathrm{4}{R}}=\frac{\mathrm{48}×\mathrm{36}}{\mathrm{2}}\Rightarrow{R}=\mathrm{26} \\ $$
Answered by cortano12 last updated on 29/Mar/24
$$\:\:\Rightarrow{x}\:.\mathrm{36}\:=\:\mathrm{24}.\mathrm{24} \\ $$$$\:\:\Rightarrow{x}\:=\:\frac{\mathrm{576}}{\mathrm{36}}=\:\mathrm{16} \\ $$$$\:\:\Rightarrow\:\underbrace{\boldsymbol{{O}}} \\ $$
Answered by som(math1967) last updated on 29/Mar/24
Commented by som(math1967) last updated on 29/Mar/24
$$\:{tan}\theta=\frac{\mathrm{24}}{\mathrm{36}}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\:{tan}\mathrm{2}\theta=\frac{\mathrm{2}×\frac{\mathrm{2}}{\mathrm{3}}}{\mathrm{1}−\frac{\mathrm{4}}{\mathrm{9}}}=\frac{\mathrm{4}}{\mathrm{3}}×\frac{\mathrm{9}}{\mathrm{5}}=\frac{\mathrm{12}}{\mathrm{5}} \\ $$$$\:\frac{\mathrm{24}}{{x}}=\frac{\mathrm{12}}{\mathrm{5}}\Rightarrow{x}=\mathrm{10} \\ $$$$\:{R}=\mathrm{36}−\mathrm{10}=\mathrm{26} \\ $$
Answered by BaliramKumar last updated on 29/Mar/24
$$\left(\mathrm{2r}\:−\:\mathrm{36}\right)\mathrm{36}\:=\:\mathrm{24}×\mathrm{24} \\ $$$$\left(\mathrm{r}−\mathrm{18}\right)\mathrm{36}\:=\:\mathrm{12}×\mathrm{24} \\ $$$$\mathrm{r}−\mathrm{18}\:=\:\mathrm{8} \\ $$$$\mathrm{r}\:=\:\mathrm{26} \\ $$
Answered by MM42 last updated on 29/Mar/24
$$\left(\mathrm{36}−{r}\right)^{\mathrm{2}} +\mathrm{24}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$\mathrm{1296}+{r}^{\mathrm{2}} −\mathrm{72}{r}+\mathrm{576}={r}^{\mathrm{2}} \\ $$$$\mathrm{72}{r}=\mathrm{1872} \\ $$$$\Rightarrow{r}=\mathrm{26} \\ $$