4. $A, B$ are two fixed points on a plane, find a point $C$ on the plane such that $\triangle A B C$ forms an isosceles triangle. There are $\qquad$ such points $C$.

将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。 

Note: The blank space represented by $\qquad$ in the original text is kept as is in the translation.
4.6. 

Translate the text above into English, please retain the original text's line breaks and format, and output the translation result directly.