The following proof is attributable to Zacharias. Denote the radius of circle $${\displaystyle \,O_{i}}$$ by $${\displaystyle \,R_{i}}$$ and its tangency point with the circle $${\displaystyle \,O}$$ by 展开

Casey's theorem and its converse can be used to prove a variety of statements in Euclidean geometry. For example, the shortest known proof of 展开

It can be seen that the four circles need not lie inside the big circle. In fact, they may be tangent to it from the outside as well. In that case, the following change should be made:
If $${\displaystyle \,O_{i},O_{j}}$$ are both tangent from the same … 展开

• Weisstein, Eric W. "Casey's theorem". MathWorld.
• Shailesh Shirali: "'On a generalized Ptolemy Theorem'". In: Crux Mathematicorum, Vol. 22, No. 2, pp. 49-53 展开