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I want to create a point at the intersection of two lines as it appears on the attached image.

enter image description here

The red line is the stream network, and the green line is the 600m contour. I use ArcGis 10.2.2

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You may use the Intersect tool and define POINT as output type.

Computes a geometric intersection of the input features. Features or portions of features which overlap in all layers and/or feature classes will be written to the output feature class.

output type: POINT - Point intersections will be returned. If the inputs are line or polygon, the output will be a multipoint feature class.

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