Students were given the following task: In a given triangle $KLM$, with a point $S$ located in its interior, find all chords of the triangle that are bisected by point $S$ (see the picture).
Students started discussing possible solutions:
Paul suggested constructing the chords as line segments perpendicular to the sides of triangle $KLM$, with endpoints on the sides and passing through point $S$.
Radek suggested constructing the chords as line segments connecting point $S$ and the vertices $K$, $L$, and, $M$ of triangle $KLM$.
Ota suggested finding the centroid of the triangle and constructing the line passing through both the centroid and point $S$. The endpoints of the chord are where this line intersects the sides of the triangle $KLM$.
Jane would reflect triangle $KLM$ through point $S$ to get triangle $K'L'M'$. The intersections of the corresponding sides of triangles $KLM$ and $K'L'M'$ would give the endpoints of the desired chord.
Who was correct?
Jane
Paul
Radek
Ota
Jane solved the task as follows: She reflected triangle $KLM$ through point $S$ to get triangle $K'L'M'$. Then, by finding the intersections of the corresponding sides of triangles $KLM$ and $K'L'M'$, she obtained the endpoints of the line segment $AB$, which is the desired chord that satisfies the conditions of the task (see the picture).
