[] , [] , [^] , []Isosceles triangle and the length of parallel segments / If not segment BC but line BC(GC World : Various problems ,Is the useless one useless?)

There is a isosceles triangle ABC. Point P is on the base BC.
Two lines which are parallel to AB and AC respectively and intersect on P are drawn.
The intersections of parallel lines with AB and AC are point Q and R respectively.
Then PQ + PR is constant.

Let's change the limitation of "on the base BC" in this theorem to "on the line BC".
What will you find?


Forum of Geometric Constructor by Y.Iijima