Area bounding - graph inequalities

https://www.geogebra.org/geometry?command=H=(5,8);I=(10,8);G=(6,10);F=(9,10);a:y<y(((F%2BG)/(2)))-sqrt((((G-F)^(2))/(4))-(x(((F%2BG)/(2))))^(2)%2B2x(((F%2BG)/(2)))x-x^(2))∧y>y(((H%2BI)/(2)))-sqrt((((H-I)^(2))/(4))-(x(((H%2BI)/(2))))^(2)%2B2x(((H%2BI)/(2)))x-x^(2));b:y<(y(H)-y(G))/(x(H)-x(G))x%2B(x(H)y(G)-x(G)y(H))/(x(H)-x(G))∧y>y((H%2BI)/2)-sqrt((((H-I)²)/4)-(x((H%2BI)/2))²%2B2x((H%2BI)/2)x-x²)∧x>x(H)∧x<x(G);c:y<(y(I)-y(F))/(x(I)-x(F))x%2B(x(I)y(F)-x(F)y(I))/(x(I)-x(F))∧y>y((H%2BI)/2)-sqrt((((H-I)²)/4)-(x((H%2BI)/2))²%2B2x((H%2BI)/2)x-x²)∧x>x(F)∧x<x(I)