1. In whatever way, and using whatever method, is appropriate for the format in which the geographic data is stored. This may be as simple as loading a single image (QImage), or something vastly more involved.
2. Get the screen coordinate the user clicked on from the widget displaying the chart (maybe QWidget::mousePressEvent, maybe something else) Do some sort of mathematics to map that value to the lat/lon of the point under the cursor. This mapping will have to take into consideration the projection of the underlying chart.
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