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### Circle of Radius 1 km around Given Latitude/Longitude

```Date: 08/27/2002 at 20:50:24
From: Simla
Subject: Circle of radius 1 Km around given latitude and longitude

Hi,

I need feed points for a circle of radius 1 km with center at a given
latitude and longitude. Eight or more points should be enough for the
program. Could you tell me what formula I should use and how to get
the points? Will I use spherical geometry?

Thanks,
Simla
```

```
Date: 08/28/2002 at 10:24:41
From: Doctor Rick
Subject: Re: Circle of radius 1 Km around given latitude and longitude

Hi, Simla.

Another inquirer wanted just four points (north, east, south, and
west), but the answer I gave will allow you to calculate as many as
you want - just choose headings such as 45 degrees.

Finding Points on the Earth
http://mathforum.org/library/drmath/view/51816.html

Since you are only concerned with short distances (1 km), a flat-earth
approximation is probably sufficient, so you might also look here:

Transformation between (x,y) and (longitude, latitude)
http://mathforum.org/library/drmath/view/51833.html

Here I explain how to convert latitude and longitude to x and y
coordinates in a flat-earth approximation:

x = R*(a2-a1)*(pi/180)*cos(b1)
y = R*(b2-b1)*pi/180

You want to do the reverse. First find the (x,y) coordinates of a
bunch of points on the circle using the usual Cartesian equation of a
circle centered at the origin:

x^2 + y^2 = r^2

Then you have to convert these (x,y) coordinates to the latitude and
longitude of each point. I don't give this transformation in the page
above, but it's easy enough to solve the equations for x and y to get
a2 and b2:

a2 = a1 + (x*180)/(R*pi*cos(b1))
b2 = b1 + (y*180)/(R*pi)

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Euclidean/Plane Geometry
High School Higher-Dimensional Geometry
High School Trigonometry

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