Question

Calculati razele cercurilor din. figura 3 stiind ca O1 O2=18cm 01 O3=14cm O2 O3=10cm.​

Answer 1

Răspuns:

r1=11cm ; r2=7cm ; r3=3cm

Explicatie:

0102=18cm =》r1+r2 =18cm

0103=14cm =》r1+r3=14cm

0203=10cm=》r2+r3=10cm

Adunând cele trei relații:

=》2(r1+r2+r3)=18cm+14cm+10cm

2(r1+r2+r3)=42 /:2

r1+r2+r3=21cm

r1+r2=18cm

=》r3=21cm-18cm = r3=3cm

r1+r3=14cm =》r1=14cm-3cm =r1=11cm

r1+r2=18cm=》r2=18cm-11cm =r3 =3cm

● Sper ca te-am ajutat!

Answer 2

$\it O_1O_2=R_1+R_2=18 \Rightarrow R_2=18-R_1\ \ \ \ \ (1)\\ \\ O_1O_3=R_1+R_3=14 \Rightarrow R_3=14-R_1\ \ \ \ \ (2)\\ \\ O_2O_3=R_2+R_3=10\ \stackrel{(1),(2)}{\Longrightarrow}\ 18-R_1+14-R_1=10 \Rightarrow 32-2R_1=10 \Rightarrow \\ \\ \Rightarrow 32-10=2R_1 \Rightarrow 22=2R_1|_{:2} \Rightarrow R_1=11\ cm\ \ \ \ \ \ (3)$

$\it (1),\ (3) \Rightarrow R_2=18-11=7\ cm\\ \\ (2),\ (3) \Rightarrow R_3=14-11=3\ cm$