How many regions are in a circle with n points?
Table of Contents
- 1 How many regions are in a circle with n points?
- 2 How many arcs are determined by n points on a circle?
- 3 What is the maximum number of regions formed by NN intersecting circles?
- 4 How many regions does a circle with 6 points have?
- 5 How many common points to the secant of the circle and circle?
- 6 How many common points are there for a tangent to a circle?
- 7 What is the maximum number Ln of regions defined by N lines in the plane?
How many regions are in a circle with n points?
If we pick three distinct points on a circle and connect each pair of them with a chord, we can form four distinct, nonintersecting regions. What is the maximum number of nonintersecting regions that we can form from the chords connecting four distinct points on a circle?
How many arcs are determined by n points on a circle?
n points on a circle determine n(n−1) distinct arcs.
How many common points to the secret of the circle and circle?
there are two common points.
What is the maximum number of regions formed by NN intersecting circles?
With n sets there are 2^n possible relations. Three intersecting circles divide the plane into 3 x (3 – 1) + 2 = 8 = 2^3 regions, but with four circles we have 14 regions, not 16!…Intersecting circles.
| n | ?(n) |
|---|---|
| 4 | 12 |
How many regions does a circle with 6 points have?
Another way to impose the “random” condition is to say that the points must be placed to get the maximum number of regions. The picture above right gives the answer 31 regions for n=6— not 32 but 31! If we add a 7th point, and count very carefully, we get 57 regions.
How many points are in a circle?
Three points
Three points uniquely define a circle. If you circumscribe a circle around a triangle, the circumcenter of that triangle will also be the center of that circle. Created by Sal Khan.
How many common points to the secant of the circle and circle?
There are two points common to the secant of the circle. A secant can overlap the circle at exactly two essential points in the specific case of a circle.
How many common points are there for a tangent to a circle?
Two
Answer: Two (iv) The common point of a tangent to a circle and the circle is called point of contact. A tangent to a circle is a line that intersects the circle at only one point and that point is called a point of contact.
How many straight lines can be drawn through 10 points on a circle?
⇒10C2=10×9×8! 2×1×8! ⇒10C2=10×92×1=45. Hence, the answer of part a) is 45 lines.
What is the maximum number Ln of regions defined by N lines in the plane?
The maximum number Ln of regions in the plane that can be defined by n straight lines in the plane is: Ln=n(n+1)2+1. This sequence is A000124 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).