Question 89
Let $\triangle ABC$ be a triangle with circumcentre $O$. The perpendicular line from $O$ to $BC$ intersects line $BC$ at $M$ and line $AC$ at $P$, and the perpendicular line from $O$ to $AC$ intersects line $AC$ at $N$ and line $BC$ at $Q$. Let $D$ be the intersection point of lines $PQ$ and $MN$. Construct the parallelogram $PCQJ$. Prove the following:
a) The points $A, B, O, P, Q, J$ are all on the same circle.
b) Line $OD$ is perpendicular to line $CJ$.
a) The points $A, B, O, P, Q, J$ are all on the same circle.
b) Line $OD$ is perpendicular to line $CJ$.