Question Number 96922 by M±th+et+s last updated on 05/Jun/20
Commented by M±th+et+s last updated on 05/Jun/20
$${prove}\:{that}:\:{r}_{\mathrm{1}} +{r}_{\mathrm{3}} +{r}_{\mathrm{5}} ={r}_{\mathrm{2}} +{r}_{\mathrm{4}} +_{\mathrm{6}} \\ $$
Commented by mr W last updated on 05/Jun/20
$${symmetry}: \\ $$$${r}_{\mathrm{1}} ={r}_{\mathrm{6}} \\ $$$${r}_{\mathrm{2}} ={r}_{\mathrm{5}} \\ $$$${r}_{\mathrm{3}} ={r}_{\mathrm{4}} \\ $$$$\Rightarrow{r}_{\mathrm{1}} +{r}_{\mathrm{3}} +{r}_{\mathrm{5}} ={r}_{\mathrm{2}} +{r}_{\mathrm{4}} +{r}_{\mathrm{6}} \\ $$
Commented by M±th+et+s last updated on 05/Jun/20
$${but}\:{the}\:{adjacent}\:\mathrm{2}\:{triangles}\:{around}\:{the} \\ $$$${right}\:{angle}\:{are}\:{not}\:{necessarily}\:{congrunet} \\ $$
Commented by mr W last updated on 05/Jun/20
$${give}\:{an}\:{example}\:{please}. \\ $$
Commented by M±th+et+s last updated on 05/Jun/20
$${yes}\:{sir}\: \\ $$$${i}\:{mean}\:{you}\:{cannot}\:{assume}\:{r}_{\mathrm{1}} ={r}_{\mathrm{6}} \\ $$$${because}\:{the}\:{circle}\:{look}\:{like}\:{same} \\ $$
Commented by M±th+et+s last updated on 05/Jun/20
$${it}\:{should}\:{be}\:{proved}\:{geometry} \\ $$
Commented by mr W last updated on 05/Jun/20
$${i}\:{did}\:{it}\:{with}\:{the}\:{word}\:``{symmetry}''. \\ $$$${it}'{s}\:{too}\:{easy}\:{to}\:{prove}\:{and}\:{also}\:{obvious}. \\ $$
Commented by mr W last updated on 05/Jun/20
