Roundabouts—give way to the right

Just to further illustrate the point to @Akrasia, using a real life example -

This is the Clough roundabout, close to Gorey in Co. Wexford. It's the route I drive when on my way home from Gorey - a journey I make at least three or four times a week.

I need to take the exit to the right. Note how there's no visibility back along that road, so I can't see anything approaching from that side which is not already at its 'Yield' sign.

I position myself where the red X is, and come to a complete halt to yield to a blue car which is already on the roundabout when I get there, and which is taking the path shown by the blue arrow.

The blue car moves on, and there's now not a single vehicle in sight. So, I begin to take the path shown by the red arrow, in order to get into the correct lane for my desired exit.

As I'm doing so, the yellow car suddenly enters the fray from the approach road to the right (point marked by the yellow X), at a speed such that its driver has to slow down when he/she sees me.

Am I wrong for having entered the roundabout when there wasn't a single vehicle to be seen?

And if so, what am I to do instead? All I can think of is either wait there indefinitely, or else take a different route home altogether.

I really am eagerly awaiting your answer on this one…..

I take the interpretation where I don't deliberately enter a roundabout when I can see a car coming from the right towards me at a speed and distance that would cause an accident if that other driver didn't take evasive action to avoid me.

I'm not trying to excuse drivers speeding through roundabouts, I'm trying to say that it's the responsibility for the driver entering the roundabout to ensure that there are no cars to his/her right that would be forced to take evasive action to avoid him/her

With regard to the first line of your response here (which is the more relevant one in actually answering the question):

What you now say yourself doesn't tally with your earlier assertion that a driver must give way to cars even approaching the roundabout from the right. This is obviously not possible if that other car is approaching from a point which you can't even see. So, it's clearly not a "must" situation.

With regard to your second line: I agree. If you can see there's a car about to enter the roundabout from your right, at a speed at which you'd create a hazard for it if you began to enter the roundabout too, then you shouldn't enter the roundabout until that other car has passed.

However, I still maintain that the driver of the other car shouldn't in the first place be entering the roundabout at a speed which may partly contribute to a hazard, should somebody else attempt to enter from the next entrance. This is in line with the general driving rule of always be able to stop safely in the distance you can clearly see ahead.