# Distance across a circle

• Feb 9th 2011, 11:04 AM
Distance across a circle
Hi there, I'm writing a computer program and I'm having a problem with the geometry. I would be very grateful for any help.
My problem is that i have one fixed point on a circles perimeter and one point which is moving around the perimeter. Do you know how i can calculate the distance between the points at any time? I should add that i know the radius and the angle at which the moving point is in relation to the fixed. Does such a formula exist?
Anyway, thanks for your time and any help would be amazing!
• Feb 9th 2011, 11:09 AM
Ackbeet
If $d$ is the distance between two points on a circle of radius $a$, and the angle subtended by the two radii to the two points is given by $\theta,$ then we can use the Law of Cosines to compute the distance:

$d^{2}=a^{2}+a^{2}-2(a)(a)\cos(\theta).$

Can you simplify?
• Feb 9th 2011, 02:09 PM
If $d$ is the distance between two points on a circle of radius $a$, and the angle subtended by the two radii to the two points is given by $\theta,$ then we can use the Law of Cosines to compute the distance:
$d^{2}=a^{2}+a^{2}-2(a)(a)\cos(\theta).$