Chứng minh rằng 1/ha+1/hb+1/hc=1/r

2S_ABC = h_a.a = h_a.b = h_c.c

Suy ra \[\frac{1}{{{h_a}}} + \frac{1}{{{h_b}}} + \frac{1}{{{h_c}}} = \frac{a}{{2S}} + \frac{b}{{2S}} + \frac{c}{{2S}} = \frac{1}{{2S}}\left( {a + b + c} \right)\]

\[ = \frac{1}{{r\left( {a + b + c} \right)}}\left( {a + b + c} \right)\](vì 2S=r(a+b+c)).

\[ = \frac{1}{r}.\]