Question 15
(NET 2) Let $ABCD$ be a convex quadrilateral whose vertices do not lie on a circle. Let $A'B'C'D'$ be a quadrangle such that $A',B',C',D'$ are the centers of the circumcircles of triangles $BCD,ACD,ABD$, and $ABC$. We write $T(ABCD)=A'B'C'D'$. Let us define $A''B''C''D''=T(A'B'C'D')=T(T(ABCD))$.
(a) Prove that $ABCD$ and $A''B''C''D''$ are similar.
(b) The ratio of similitude depends on the size of the angles of $ABCD$. Determine this ratio.
(a) Prove that $ABCD$ and $A''B''C''D''$ are similar.
(b) The ratio of similitude depends on the size of the angles of $ABCD$. Determine this ratio.