Distance across a circle

**tannadice** · February 9th 2011, 10:04 AM

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!

**Ackbeet** · February 9th 2011, 10:09 AM

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?

**tannadice** · February 9th 2011, 01:09 PM

Originally Posted by 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?

Thank you very much this is just what i'm looking for. I couldn't find the right expression anywhere. Thanks for your time and help!!

**Ackbeet** · February 9th 2011, 01:10 PM

You're welcome. Have a good one!

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