Question 71
Let be given an acute triangle $ABC$ inscribed in a circle with center $O$ and two points $M$, $N$ on the line $AC$ such that $\overline{MN} = \overline{AC}$. Let $D$ be the orthogonal projection of $M$ on the line $BC$, $E$ be that of $N$ on the line $AB$.
1/ Prove that the orthocenter $H$ of triangle $ABC$ lies on the circumcircle with the center $O'$ of triangle $BED$.
2/ Prove that the midpoint of segment $AN$ is symmetric to $B$ with respect to the midpoint of segment $OO'$.
1/ Prove that the orthocenter $H$ of triangle $ABC$ lies on the circumcircle with the center $O'$ of triangle $BED$.
2/ Prove that the midpoint of segment $AN$ is symmetric to $B$ with respect to the midpoint of segment $OO'$.