Why does a Star looks smaller than the Sun?

Why do objects look smaller when they are far way? I was led into this question while pondering about why stars are only pinpoints of light, and the sun is as big as it is.

This will seem like a trivial question, maybe it is. Maybe you already have the understanding that I don't. Maybe the only non-trivial thing here is the way I am looking at the question, which is geometrically.

Think of it as an eight year old, keep on asking the whys. Shed all your preconceived ideas and intuitions and instincts that you may have built over all these years, and then you may see what I want to show.

Lets talk only in simple geometry.

Let AB be a thing. There be an observer eye E₁ and another, much farther away, E₂. The gray lines are rays of light from endpoints A and B. The height of AB does not change with respect to the distance to E₁ or E₂. Geometrically, the height is fixed. The only variable here seems to be the angle at which light rays are incident on E. But what should that matter? How can we reconcile the fact that the height not just looks but is different to the observers?

I hope I was able to convey my conundrum.

A brief thought came to my mind about something having to do with the eye, the lens, the retina forming an image. But it seemed so preposterous an idea - how could the universe (in a sense) depend on one of these internal organs of a mortal being. That if I had better eyes I would be able to see the storms on the sun. It might be true, but I suspect it wouldn't change the size but only the resolution. In any case, the answer I seek should be in geometry somewhere.

After staring at blank spaces, my hand, stuff in the background, remembering the recent solar eclipse, moving my hand back and forth against the bookshelf - I thought of a certain geometrical significance of the incident angle. I also briefly paused to acknowledge a possible frown on someone who chanced to look at my window moments ago.

So if you consider this:

Two objects AB and XY are again of the same height to both E₁ and E₂. But, there it is. Geometrically, because of the difference in incident ray's angle, the shadow of XY on AB are of different sizes. AXE₁-BYE₁ is greater than AXE₂-BYE₂. Only by the virtue of straight lines and geometry, E₂ can see more parts of AB than E₁. But still, it doesn't explain different heights.

In any case, this kind of emphasized the idea that I think was always there somewhere, when I was slowly moving back and forth, my right-hand-index-finger to my left-hand-flattened-palm. I could see that my palm was covering more area around the index finger when they were close, and vis-versa. This preceding statement seems a little ambiguous, and so was the thought. My palm covering more area of what - the sight? And how could that impact the size of the object?

After a little more brooding, it became clear.  Palm was covering the sphere of vision, vision not in the sense of eyes, perception or sight. But in the sense of being. Maybe I should call it something else, the sphere of being.

So AB blocks more area on the circle of E₁ (SOB₁) than on circle of E₂ (SOB₂). And one could say the height of AB is in fact not absolute but relative, at least seems to be, relative to these circles. In other words it is relative to what else is out there. The circle is ever expanding, infinite. 

A closer object lies on the smaller circle/sphere of being. The lines that represent sun and star below are copies - same length. But the sun is like a blot on observer's circle, and the star a pinpoint. 

And as the circle expands, the same line will disappear into one of the infinite dots.

It is interesting to note that something tangible like size could be relative. And kind of ironical that the mortal being is at the center of it.

Now the following is not without an assumption, but if you can accommodate a slight modification in the definition of the term 'size', which to be fair, is intuitive enough, the following will make sense. 

Geometrically, if the size of an object is the area that it covers on observer's circle of being, then the object's size is inversely proportional to the size of the C/SOB, which depends directly on the radius of the C/SOB, which, in conclusion, is the distance between the two.