# Coordinates of point inside of circle

I'm sorry if what I'm asking has already been answered or is really easy but I struggled a little and haven't been able to come up with an idea.

TThe context is as follows: a robot is being placed inside a circle. I need to find the position the robot is being placed given that I know the center and the radius of the circle and that I have a distance sensor which gives me the distance to a point on the circle circumference.

I believe there isn't enough information to calculate this point. If that is indeed the case could you please point me to the kind of information i'm missing?.

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If the circle has radius $r$ and the robot measures distance $d<r$ to the circumference, then all you can say is that the robot is on the circle of radius $r-d$ around the center. – Hagen von Eitzen Oct 21 '12 at 14:42
@Hagen: It says "distance to a point on the circumference", not "distance to the circumference". It's not clear in the question whether this is the distance to a fixed point, or to the nearest point, or to an arbitrary point, and if arbitrary, whether the sensor can be used more than once. – joriki Oct 21 '12 at 17:01
the distance is to an arbitrary point that gets picked by the senzor – Jack Blaze Oct 22 '12 at 16:29

Well it depends what the problem means, it is a little vague as it is stated.

Does you distance sensor gives you the distance to a fixed point on the circle? Or can you use it multiple times to get the distance to more points on the circle?

Note that if you can use the sensor twice, for two fixed points on the circle, then you can most of the time determine the point (what I mean by most of the time is that if the two points are diametrally opposed you can only reduce the problem to two possibilities, while if the two points are closed you can find the robot)... Three points always determine the possition, no matter which three points are....

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thanks for the hint search . after the first 5 seconds the robot is allowed to move so more samples could be gathered however there is no guarantee that the would come from different points of the circumference – Jack Blaze Oct 22 '12 at 16:32

In this question, you are basically trying to set up a co-ordinate system. For this, you need two things: 1. Origin 2.A fixed line (to function as your X Axis).

While you do have the origin, you need to set a line as your fixed axis.

Once you have set up the fixed line, you could use trigonometry (polar co ordinates) to find the position of the required point.

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your ideea seems interesting to pursue can you elaborate a bit on that? thanks. – Jack Blaze Oct 22 '12 at 16:32
If we had a compass with no N/S/E/W directions marked on it, we would be confused as to which direction was which. We would need one mark on the compass pointing North to guide us. This would tell us that the point opposite the North was south, 45* left of it was North East and so on. Similarly, in your question, we would need the X axis to help us 'fix' the co-ordinate system – RahulHP Oct 23 '12 at 4:52
Once we have fixed the X axis, we can then use polar co ordinates (r cos(theta), r sin(theta)) to obtain the information about the point – RahulHP Oct 23 '12 at 4:56