Prove the area of the blue triangle is $$ \frac{1}{\sqrt{ \left(\frac{1}{h_a}+\frac{1}{h_b}+\frac{1}{h_c}\right) \left(\frac{1}{h_a}+\frac{1}{h_b}-\frac{1}{h_c}\right) \left(\frac{1}{h_b}+\frac{1}{h_c}-\frac{1}{h_a}\right) \left(\frac{1}{h_c}+\frac{1}{h_a}-\frac{1}{h_b}\right) }} $$