the maximum number of points of intersection of three lines taking two at a time is?how?

The maximum numbers points of intersection of three lines (let lm and n) taken two at a time is three. This can be shown below

Here, the three points A, B and C are the point of intersection of the lines.

https://s3mn.mnimgs.com/img/shared/userimages/mn_images/image/Tr1.png

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five 

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 Intersecting lines

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