Dane na rysunku.
Wyznaczenie y i r:
[tex]\left \{ {{y=2x-r} \atop {y=r-x}} \right.\\r-x=2x-r\\r+r=2x+x\\2r=3x\quad|:2\\r=\dfrac{3}{2}x\\y=\dfrac{3}{2}x-x=\dfrac{1}{2}x[/tex]
Wyznaczenie h:
[tex]h^2=r^2-y^2\\h^2=\left(\dfrac{3}{2}x\right)^2-\left(\dfrac{1}{2}x\right)^2\\h^2=\dfrac{9}{4}x^2-\dfrac{1}{4}x^2\\h^2=\dfrac{8}{4}x^2\\h^2=2x^2\\h=x\sqrt{2}[/tex]
Obliczenie x:
[tex]P=24\sqrt{2}\\P=\dfrac{ah}{2}\\a=x+2x=3x[/tex]
[tex]24\sqrt{2}=\dfrac{3x\cdot x\sqrt{2}}{2}\\24\sqrt{2}=\dfrac{3x^2\sqrt{2}}{2}\quad|\cdot2\\48\sqrt{2}=3x^2\sqrt{2}\quad|:3\\16\sqrt{2}=x^2\sqrt{2}\quad|:\sqrt{2}\\16=x^2\\x=4[/tex]
Obliczenie r:
[tex]r=\dfrac{3}{2}x=\dfrac{3}{2}\cdot4=3\cdot2=6[/tex]
Obliczenie pola koła:
[tex]P_k=\pi r^2[/tex]
[tex]P_k=\pi\cdot6^2=36\pi[/tex]
