Question-96922

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_1 =r_6 r_2 =r_5 r_3 =r_4 ⇒r_1 +r_3 +r_5 =r_2 +r_4 +r_6

$${symmetry}: \\ $$$${r}_{\mathrm{1}} ={r}_{\mathrm{6}} \\ $$$${r}_{\mathrm{2}} ={r}_{\mathrm{5}} \\ $$$${r}_{\mathrm{3}} ={r}_{\mathrm{4}} \\ $$$$\Rightarrow{r}_{\mathrm{1}} +{r}_{\mathrm{3}} +{r}_{\mathrm{5}} ={r}_{\mathrm{2}} +{r}_{\mathrm{4}} +{r}_{\mathrm{6}} \\ $$

Commented by M±th+et+s last updated on 05/Jun/20

but the adjacent 2 triangles around the right angle are not necessarily congrunet

$${but}\:{the}\:{adjacent}\:\mathrm{2}\:{triangles}\:{around}\:{the} \\ $$$${right}\:{angle}\:{are}\:{not}\:{necessarily}\:{congrunet} \\ $$

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_1 =r_6 because the circle look like same

$${yes}\:{sir}\: \\ $$$${i}\:{mean}\:{you}\:{cannot}\:{assume}\:{r}_{\mathrm{1}} ={r}_{\mathrm{6}} \\ $$$${because}\:{the}\:{circle}\:{look}\:{like}\:{same} \\ $$

Commented by M±th+et+s last updated on 05/Jun/20