Question 63
Let be given a convex quadrilateral **ABCD**. A point **M** moves on the line **AB** but does not coincide with **A** and **B**. Let **N** be the second point of meeting (distinct from **M**) of the circles (**MAC**) and (**MBD**). Prove that
i) $N$ moves on a fixed circle,
ii) The line $MN$ passes through a fixed point.
(The symbol $(XYZ)$ denotes the circle passing through the points $X$, $Y$, $Z$.)
i) $N$ moves on a fixed circle,
ii) The line $MN$ passes through a fixed point.
(The symbol $(XYZ)$ denotes the circle passing through the points $X$, $Y$, $Z$.)