Question 64
Let $ABCD$ be an inscribed convex quadrilateral with diagonals $AC$ and $BD$. Each of the four vertices is reflected on the diagonal it does not lie on.
Prove that the resulting four points lie on a common circle or a common line.
a. Investigate when the four resulting points lie on a common line and give a simple equivalent condition for the quadrilateral $ABCD$.
b. Prove that in all other cases, the four resulting points lie on a common circle.
Prove that the resulting four points lie on a common circle or a common line.
a. Investigate when the four resulting points lie on a common line and give a simple equivalent condition for the quadrilateral $ABCD$.
b. Prove that in all other cases, the four resulting points lie on a common circle.