# Thread: How do I measure the distance between two points on a euclidean graphed circle?

1. ## How do I measure the distance between two points on a euclidean graphed circle?

So I have a circle defined in a euclidean plane, how do I measure the distance along the circle between any two given points on the circle?

The specific circle that I'm looking at right now is defined by the equation:

(x-1280)^2 + (y-800)^2 = 422500

thank you.

2. Have you considered the radius, the value of $\displaystyle \pi$, and the proportion of the circle cut out by the wedge formed by the center and the two points?

3. Hello, Egoist!

So I have a circle defined in a euclidean plane.
How do I measure the distance along the circle
between any two given points on the circle?

The specific circle that I'm looking at right now is defined by the equation:
. . $\displaystyle (x-1280)^2 + (y-800)^2 \:=\: 422500$
The center of the circle is: .$\displaystyle C(1280,800)$
The radius is: .$\displaystyle r \:=\:650$

Suppose the two given points are: .$\displaystyle P(x_1,y_1),\;Q(x_2,y_2)$

Find the slope of $\displaystyle CP\!:\;\;m_1 \:=\:\frac{y_1-800}{x_1-1280}$

Find the slope of $\displaystyle CQ\!:\;\;m_2 \:=\:\frac{y_2-800}{x_2-1280}$

The angle $\displaystyle \theta$ between the two radii is given by: .$\displaystyle \tan\theta \:=\:\frac{m_2-m_1}{1 + m_1m_2}$
. . Find $\displaystyle \theta$ in radians.

The arc length between $\displaystyle P$ and $\displaystyle Q$ is: .$\displaystyle s \;=\;r\theta$

4. Originally Posted by Soroban
Hello, Egoist!

The center of the circle is: .$\displaystyle C(1280,800)$
The radius is: .$\displaystyle r \:=\:650$

Suppose the two given points are: .$\displaystyle P(x_1,y_1),\;Q(x_2,y_2)$

Find the slope of $\displaystyle CP\!:\;\;m_1 \:=\:\frac{y_1-800}{x_1-1280}$

Find the slope of $\displaystyle CQ\!:\;\;m_2 \:=\:\frac{y_2-800}{x_2-1280}$

The angle $\displaystyle \theta$ between the two radii is given by: .$\displaystyle \tan\theta \:=\:\frac{m_2-m_1}{1 + m_1m_2}$
. . Find $\displaystyle \theta$ in radians.

The arc length between $\displaystyle P$ and $\displaystyle Q$ is: .$\displaystyle s \;=\;r\theta$

Thank you very much! BTW, as you can see, I'm new here, how do I "officially" thank you?