Pedal triangle

[ins-]

Let ABC is an acute-angled triangle and A1, B1, C1 are the feets of altitudes from the verices A, B, C respectively.
Is it possible to express the area of A1B1C1 in therms of the areas of the triangles AB1C1, A1BC1, A1B1C?

[vvsss]

s^3 + (s1+s2+s3) s^2 = 4 s1 s2 s3 следует из si = s0 cos^2 alpha i

[ins-]

Is it possible to use: $cos^2A+cos^2B+cos^2C+2cosAcosBcosC=1$?