Question Number 200761 by a.lgnaoui last updated on 23/Nov/23
$$\boldsymbol{\mathrm{Determiner}}\:\:\boldsymbol{\mathrm{r}}\:\:\mathrm{et}\:\:\boldsymbol{\mathrm{R}}\:\:\left({voir}\:{figure}\:\right) \\ $$$$\:\mathrm{Sachant}\:\mathrm{aue}:\measuredangle\boldsymbol{\mathrm{C}}=\mathrm{120}\:\::\boldsymbol{{AB}}=\mathrm{12} \\ $$
Commented by a.lgnaoui last updated on 23/Nov/23
Commented by mr W last updated on 23/Nov/23
$${do}\:{you}\:{mean}\:``{r}=?\:{and}\:{R}=?''\:{or} \\ $$$$``{r}+{R}=?''\:? \\ $$
Commented by a.lgnaoui last updated on 23/Nov/23
$$\mathrm{find}\:\boldsymbol{\mathrm{r}}\:\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{R}} \\ $$
Commented by a.lgnaoui last updated on 23/Nov/23
$$\left(\boldsymbol{\mathrm{A}}\:\mathrm{and}\:\boldsymbol{\mathrm{B}}\:\mathrm{are}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{circle}\::\mathrm{radius}\:\boldsymbol{\mathrm{r}}\right)\: \\ $$
Commented by mr W last updated on 23/Nov/23
$${i}\:{think}\:{you}\:{can}\:{not}\:{determine}\:{r}\:{and} \\ $$$${R}.\:{you}\:{can}\:{only}\:{determine}\:{the}\:{sum} \\ $$$${of}\:{r}\:{and}\:{R},\:{i}.{e}.\:{r}+{R}. \\ $$
Answered by mr W last updated on 23/Nov/23
$${AC}={r}+{R}−\mathrm{5} \\ $$$${BC}={r}+{R}−\mathrm{3} \\ $$$${say}\:{s}={r}+{R} \\ $$$$\left({s}−\mathrm{5}\right)^{\mathrm{2}} +\left({s}−\mathrm{3}\right)^{\mathrm{2}} +\left({s}−\mathrm{5}\right)\left({s}−\mathrm{3}\right)=\mathrm{12}^{\mathrm{2}} \\ $$$$\mathrm{3}{s}^{\mathrm{2}} −\mathrm{24}{s}−\mathrm{95}=\mathrm{0} \\ $$$${s}=\frac{\mathrm{12}+\sqrt{\mathrm{429}}}{\mathrm{3}}\approx\mathrm{10}.\mathrm{9} \\ $$
Commented by a.lgnaoui last updated on 26/Nov/23
$$\mathrm{thanks} \\ $$