Three

Three points are given: A (-3, 1), B (2, -4), C (3, 3)
a) Find the perimeter of triangle ABC.
b) Decide what type of triangle the triangle ABC is.
c) Find the length of the inscribed circle

Correct answer:

o =  20.4667
x = RR
k =  13.7293

Step-by-step explanation:

$$\begin{gathered} A=(-3,1) \\ B=(2,-4) \\ C=(3,3) \\ a=\sqrt{(B_x-C_x{)}^2+(B_y-C_y{)}^2}=\sqrt{(2-3{)}^2+((-4)-3{)}^2}=5\sqrt{2}\doteq 7.0711 \\ b=\sqrt{(A_x-C_x{)}^2+(A_y-C_y{)}^2}=\sqrt{((-3)-3{)}^2+(1-3{)}^2}=2\sqrt{10}\doteq 6.3246 \\ c=\sqrt{(A_x-B_x{)}^2+(A_y-B_y{)}^2}=\sqrt{((-3)-2{)}^2+(1-(-4){)}^2}=5\sqrt{2}\doteq 7.0711 \\ o=a+b+c=7.0711+6.3246+7.0711=20.4667 \end{gathered}$$

$$\begin{gathered} a=c \\ x=RR \end{gathered}$$

$$\begin{gathered} v=\sqrt{a^2-(b/2{)}^2}=\sqrt{7.0711^2-(6.3246/2{)}^2}=2\sqrt{10}\doteq 6.3246 \\ S=\frac{c\cdot v}{2}=\frac{7.0711\cdot 6.3246}{2}=10\sqrt{5}\doteq 22.3607 \\ r=2\cdot S/o=2\cdot 22.3607/20.4667\doteq 2.1851 \\ k=2\pi \cdot r=2\cdot 3.1416\cdot 2.1851=13.7293 \end{gathered}$$

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