Question

Any one can help me??? How to find the center angle of a circle . Given, center (XC, YC), two points P1(x1,y1) and P2 (x2,y2). How to find the angle between this two line which meets at the center.

Answer 1

id convert the idea to vector

Answer 2

the angle between 2 vectors:

\[cos(a)=\frac{u.v}{|u||v|}\]

Answer 3

since the |u||v| are equal thats just the radius squared

Answer 4

\[a=cos^{-1}\frac{(X-P_1).(X-P_2)}{r^2}\]

Answer 5

come to think of it, it might be better to define u and v when the center is at the origin; so subtract X from the points

Answer 6

\[a=cos^{-1}\left(\frac{(x_1-x_c)(x_2-x_c)+(y_1-y_c)(y_2-y_c)}{\sqrt{(x_1-x_c)^2+(y_1-y_c)^2}}\right)\]

that might be right .. never tried to write it out like this before

Answer 7

we can test it out with P1(0,1) and P2(1,0) this forms a 90 degree angle with a radius of 1

\[a=cos^{-1}(\frac{0+0}{1})\]

\[a=cos^{-1}(0)=pi/2\]

Answer 8

seems to work

Answer 9

thanks