Question 50
A sphere of radius $r$ is inscribed to a tetrahedron. If the altitudes of the tetrahedron are $v_1$, $v_2$, $v_3$ and $v_4$, prove
$$
\frac{1}{v_1} + \frac{1}{v_2} + \frac{1}{v_3} + \frac{1}{v_4} = \frac{1}{r}.
$$
$$
\frac{1}{v_1} + \frac{1}{v_2} + \frac{1}{v_3} + \frac{1}{v_4} = \frac{1}{r}.
$$