Question 74
Let $H$ be the orthocenter of the triangle $\triangle ABC$ and $A_1$, $B_1$, $C_1$ be the feet of the altitudes from $A$, $B$, $C$ respectively.
Find $\frac{\overline{AH}}{HA_1} \cdot \frac{\overline{BH}}{HB_1} \cdot \frac{\overline{CH}}{HC_1}$ if $\frac{\overline{AH}}{HA_1} + \frac{\overline{BH}}{HB_1} + \frac{\overline{CH}}{HC_1} = 2008$.
Find $\frac{\overline{AH}}{HA_1} \cdot \frac{\overline{BH}}{HB_1} \cdot \frac{\overline{CH}}{HC_1}$ if $\frac{\overline{AH}}{HA_1} + \frac{\overline{BH}}{HB_1} + \frac{\overline{CH}}{HC_1} = 2008$.