Question 65
Let $T$ be any point inside the square $A B C D$, and the points $A^{\prime}, B^{\prime}, C^{\prime}$ and $D^{\prime}$ be the other intersections of the lines $T A, T B, T C$ and $T D$ with the circumscribed circle of the square $A B C D$. Prove that $|A^{\prime} B^{\prime}| \cdot |C^{\prime} D^{\prime}| = |A^{\prime} D^{\prime}| \cdot |B^{\prime} C^{\prime}|$.