三弦定理和Ptolemy定理等价

The Tri chord Theorem and Ptolemy's Theorem are Equivalent to Each Other

利用正弦定理极为简单地证明三弦定理和Ptolemy定理等价 ,为完整起见 。

In this paper,by using Sine law,it is shown that the Tri chord Theorem and Ptolemy's Theorem are equivalent to each other.A short but tricyky geometric proof of Ptolemy's Theorem is given for the sake of the reference.As an interesting application,an elegant area formula of cyclic quadrilateral in term of its four sides is derived.It is a generalization of the well known Heron's formula which gives the area of a trianglein terms of its three sides.\;