Question 68
In triangle $ABC$ with orthocenter $H$ one has that
$$
AH \cdot BH \cdot CH = 3 \text{ and } AH^2 + BH^2 + CH^2 = 7
$$
Find:
a) the circumradius of $\triangle ABC$;
b) the sides of $\triangle ABC$ with maximum possible area.
$$
AH \cdot BH \cdot CH = 3 \text{ and } AH^2 + BH^2 + CH^2 = 7
$$
Find:
a) the circumradius of $\triangle ABC$;
b) the sides of $\triangle ABC$ with maximum possible area.