Question 85
Starting with three points $A$, $B$, $C$ in general position and the circumcircle $k$ of $\triangle ABC$, a step consists of drawing a line $l$ and obtaining all points of intersection of $l$ with the lines already drawn and with $k$, where $l$ is
(1) the line through two distinct points that had been obtained before or
(2) the bisector of an angle $\angle XYZ$, where $X$, $Y$, $Z$ are three previously obtained distinct points on $k$.
Is it always (i.e., for any choice of $A$, $B$, $C$) possible to obtain the orthocentre of $\triangle ABC$ in a finite number of steps?
(1) the line through two distinct points that had been obtained before or
(2) the bisector of an angle $\angle XYZ$, where $X$, $Y$, $Z$ are three previously obtained distinct points on $k$.
Is it always (i.e., for any choice of $A$, $B$, $C$) possible to obtain the orthocentre of $\triangle ABC$ in a finite number of steps?