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

In summary, the conversation discusses how the radius of a circle is typically uniform around the circle when it is at the center. However, if the radius is shifted away from the center, called r', there is a way to determine the minimum length, L, between the point and the side of the circle using the known original radius, r, and the angle, θ, between r' and L. The attached image provides clarification and drawing connections between points can help with the trigonometry needed to find L.
  • #1
hm_tested
1
0
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.
 

Attachments

  • radiusproblem.png
    radiusproblem.png
    6.1 KB · Views: 536
Mathematics news on Phys.org
  • #2
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.
 
  • #3
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
 

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

1. What is the definition of a radius not centered in a circle?

A radius not centered in a circle is the distance between the center of the circle and any point on the circumference that is not the center. In other words, it is the length of a line segment that connects the center of the circle to a point on the edge of the circle.

2. How do you find the length of a radius not centered in a circle?

To find the length of a radius not centered in a circle, you can use the Pythagorean theorem. First, measure the distance from the center of the circle to the point on the circumference. Then, measure the distance from the center to the edge of the circle along a line perpendicular to the first distance. Finally, use the Pythagorean theorem (a² + b² = c²) to find the length of the radius.

3. Can a radius not centered in a circle be negative?

No, a radius cannot be negative. The length of a radius is always a positive value, as it represents a distance.

4. How does the position of the radius affect its length?

The position of the radius does not affect its length. The length of a radius is solely determined by the distance from the center of the circle to a point on its circumference.

5. Can you find the length of a radius not centered in a circle without knowing the circle's center?

Yes, you can find the length of a radius not centered in a circle without knowing its center. As long as you have the distance from the center to the point on the circumference, you can use the Pythagorean theorem to calculate the length of the radius.

Similar threads

B Circle tangent to two lines and another circle
    • General Math
Replies
2
Views
345
MHB Finding the Center of a Circle
    • General Math
Replies
3
Views
896
MHB Formula to find arc radius using arc length, chord length, and/or segment angle
    • General Math
Replies
4
Views
4K
MHB What is the Center and Radius of a Circle?
    • General Math
Replies
9
Views
2K
MHB What caused the wrong answer for determining the center and radius of Circle 2?
    • General Math
Replies
4
Views
1K
Length of a line between origin and edge of a circle
    • General Math
Replies
4
Views
2K
A Find a circle inside of and tangent to a larger circle
    • General Math
Replies
23
Views
3K
MHB Find Center and Radius of Circle
    • General Math
Replies
2
Views
1K
B Finding Radius from chord length and tangent distance
    • General Math
Replies
13
Views
2K
I Dimension of an Angle: Clarifying the SI Standard
    • General Math
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top