Question

Calculati raza cercului inscris in triunghiul ABC si raza cercului circumscris triunghiului ABC daca AB=16 cm , AC=12 cm si BC=20 cm .

Answer 1

$p= \frac{a+b+c}{2} = \frac{12+16+20}{2}=24 \\ r= \sqrt{ \frac{(p-a)(p-b)(p-c)}{p}} = \sqrt{ \frac{12*8*4}{24}}= \sqrt{16} \\ r=4 \\ \\ 2Rr= \frac{abc}{a+b+c}= \frac{12*16*20}{12+16+20}= \frac{3840}{48}=80 \\ R= \frac{80}{2r}= \frac{80}{2*4}= \frac{80}{8} \\ R=10$