How to resize an image without changing the corner radius:

Use a rounded rectangle to fix the rounded corner radius (within a certain range)

We select the Rounded Rectangle Tool

Draw a rounded rectangle and set the rounded corner radius value in the properties panel.

Look at the current corner radius value is 9 pixels

We drag in an image and place it on top of the rounded rectangle layer

​​Select the layer menu to create a clipping mask (if you click it, it will release the clipping mask), or you can directly press Ctrl + Alt + G to clip the upper layer into the lower layer.

After we adjust the image size (it is best to keep the image as a smart object, so that the image size can be adjusted at any time without distortion), link the 2 image layers and the rounded rectangle layer.

We copy these two layers for reference, transform the layer, and change the size of the graphic and the rounded rectangle at the same time. See that the rounded corner radius is still 9 pixels, unchanged.

The rounded corners remain unchanged within a certain range. We adjust the rounded corners to the maximum, that is, two rounded corners can form a semicircle.

​ ​Look at our extreme reduction, the fillet radius finally changed. Because the diameters of the semicircle and the rounded rectangle are the same, and the rounded rectangle shrinks, the diameter of the semicircle also shrinks, and the radius of the fillet must also shrink. (Haha, but this situation is rare.)

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