[tex]bc = a^{2} \rightarrow 2R.sinB.2R.sinC=(2R.sina)^2\rightarrow 4R^2.sinBsinC=4R^2sin^2a \\\Rightarrow sinBsinC=sin^2a[/tex]
[tex]S=\frac{1}{2}a.h_a=\frac{1}{2}b.h_b=\frac{1}{2}c.h_c\\\rightarrow 2S=a.h_a=b.h_b=c.h_c\\\rightarrow a^2.h_a^2=bc.h_b.h_c\\\rightarrow h_a^2=h_b.h_c[/tex]