High School How to find a length of a "radius" not centered in a circle?

[hm_tested]

Generally in a circle, the radius of the circle is uniform around the circle due to it being at the center, this is the obvious part. However, let's say the the radius was shifted away from the center so that it is somewhere in the circle, in this case called r'. Given that the original radius, r, is known, r' is the minimum length between the point and the side of the circle, and the angle, θ, is known such that it is the angle between r' and the desired length, L, is it possible to determine L? See the attached image for clarification.

 

[mfb]

Sure. Drawing connections from the left point to the center and to the upper end of r' should help. A bit of trigonometry with the formed triangles will lead to L.

 

[hyunxu]

Try joining r' and r.It's seems that r is centre here.You need to work with theta and r' to get answer L