**Answer**

They are not perfectly round because InDesign’s graphic model does not use circle fragments; all circles and circle sections are created with Bézier curves, and ((in)famously) with these you cannot draw a perfect circle, only approximate it. This is also the case in Illustrator:

*Fig. 1. Illustrator circle and rounded corners*

But there are various levels of accuracy in “approximating”.

Circles are done the same as in Illustrator, but for the Rounded Corner option, the InDesign engineers chose the easiest – and most naïve – solution: add a single Bézier control point at the intersection of the horizontal and vertical lines:

*Fig. 2. InDesign’s circle and rounded corners*

As can be seen in the zoomed-in image, this is off in both outwards (at the starts and end) and inwards (at the outermost point) directions.

*Fig. 3. The intersection of a circle and a rounded corner at a modest 800% zoom*

However, mathematically speaking, the nearest approximate of a Bézier curve to a quarter circle segment needs its control points at a horizontal and vertical distance of `4*(Math.sqrt(2)-1)/3`

~ 0.5523 and not 1.000 (related Stack Overflow question; the article *Approximating Circular Arcs with Cubic Splines* by Philip Todd (PDF) discusses the accuracy of a number of approaches).

We can only wonder why the more accurate approximation *is* used in Adobe InDesign for circles but not for rounded corners, while in Adobe Illustrator it is used for both.

**Attribution***Source : Link , Question Author : curious , Answer Author : Jongware*