Find the relation between the circumradius of an obtuse angled triangle and its orthic triangle.
I tried using angles in the orthic triangle and sine law but getting stuck. Please help me. Would appreciate if you would give the relation using sine laws.
I got the radius is equal to $\frac{R}{2}$.
The hint:
We can assume that our triangle is acute-angled triangle and see my solution of the following problem.
A question with a triangle and its orthocenter in the picture.
Let $\measuredangle ABC>90^{\circ}$, $AA_1$, $BB_1$ and $CC_1$ be altitudes of $\Delta ABC$.
Thus, $\Delta AHC$ is an acute-angled triangle and the circumrarius of $\Delta ABC$ is equal to the circumradius of $\Delta AHC$ and since $\Delta A_1B_1C_1$ is an orthic triangle of $\Delta ABC$ and of $\Delta AHC$,
we obtain that the circumradius of the orthic triangle equal to $\frac{R}{2}$.