Question

Calculati raza cercului inscris in triunghiul ABC daca:

Answer 1

Explicație pas cu pas:

a)

AC² = BC²-AB² = 5²-3² = 25-9 = 16 = 4²

=> AC = 4 cm

$r = \dfrac{c_{1} + c_{2} - ip}{2} = \dfrac{AB+AC-BC}{2} = \\ = \dfrac{3 + 4 - 5}{2} = \dfrac{2}{2} = \bf 1 \ cm$

b)

AC² = AB²-BC² = 20²-12² = 400-144 = 256 = 16²

=> AC = 16 cm

$r = \dfrac{c_{1} + c_{2} - ip}{2} = \dfrac{AB+BC - AC}{2} = \\ = \dfrac{16 + 12 - 20}{2} = \dfrac{8}{2} = \bf 4 \ cm$

Answer 2

a)

$\it (3,\ \ 4,\ \ 5) \ triplet\ \ pittagoreic\ \Rightarrow AB=3cm,\ AC=4cm,\ BC=5cm\ .\\ \\ r=\dfrac{AB+AC-BC}{2}=\dfrac{3+4-5}{2}=\dfrac{2}{2}=1\ cm$

b)

$\it (12,\ \ 16,\ \ 20) \ triplet\ \ pittagoreic\ \Rightarrow BC=12cm,\ AC=16cm,\ A B=20cm\ .\\ \\ r=\dfrac{BC+AC-AB}{2}=\dfrac{12+16-20}{2}=\dfrac{8}{2}=4\ cm$

$\bf\underline{ Remarc\breve a}:\\ \\ \it r=\dfrac{c_1+c_2-ip}{2}$