Question 2
(CAN 2) Let triangle $ABC$ be such that its circumradius $R$ is equal to $1$. Let $r$ be the inradius of $ABC$ and let $p$ be the inradius of the orthic triangle $A'B'C'$ of triangle $ABC$.
Prove that $p\le1-\frac13(1+r)^2$.
Remark. The orthic triangle is the triangle whose vertices are the feet of the altitudes of $ABC$.
Prove that $p\le1-\frac13(1+r)^2$.
Remark. The orthic triangle is the triangle whose vertices are the feet of the altitudes of $ABC$.