[i]Create mathematical problems in a dynamic GeoGebra environment, which include the geometric figure arbelos.[/i]

By using GeoGebra, prove geometrically that the area of arbelos  [i][math]F[/math][/i][br][center][b][i] [br][math]F=\frac{\pi}{2}\left(r^2-r_1^2-r_2^2\right)[/math],[/i][/b][/center][b][br][/b][i]where [math]r,r_1,r_2[/math]  are radii of the semicircles [math]k,k_1,k_2[/math][/i] [i] respectively, and [math]r=r_1+r_2[/math][/i][i].[/i]

[center][math]F\left(k\right)=\pi r^2[/math][br][br][math]F=\frac{1}{2}\left(F\left(k\right)-F\left(k_1\right)-F\left(k_2\right)\right) [/math][br][br][math]F=\frac{\pi }{2}\left(r^2-r_1^2-r^2_2\right)[/math][/center]