Given a ∆PQR, what is the locus of points that are equidistant from R at a distance QR?

idk, maybe a circle with center R and and a radius QR? Like this:

Question

Given a ∆PQR, what is the locus of points that are equidistant from R at a distance QR? 

idk, maybe a circle with center R and and a radius QR? Like this:

aroub · Answer

|dw:1352470604128:dw| 

I know it looks so wrong, but this what I could think of ._.

anonymous · Answer

I think you are right but I'm not sure why they needed a triangle for that they could just use a line

phi · Answer

you can check your reasoning like this.  Pick a point on the circle.  How far is it from point R?
By construction, it is RQ away from point R.  So your circle meets the requirement

phi · Answer

On the other hand, pick any point not on the circle.  Then (by definition) that point is not RQ away from point R.  It is either further away or closer.  So only the points on the circle work.

anonymous · Answer

they just wrote the definition of radius more or less but why they added the triangle that's what I don't understand

phi · Answer

why they added the triangle ?

Either to confuse people, or the sentence does not mean what I think it means. I'm going with the first option.

aroub · Answer

So I have to use construction in here too? -.- But what I did is correct, right?

anonymous · Answer

I believe so :)

aroub · Answer

Thank you!!

phi · Answer

why they added the triangle ?
or maybe there are other parts to the question that use this triangle?

aroub · Answer

No, there isn't any other parts. Maybe they just want to confuse us..