# how to find mid point of an arc?

I have start point $(x_1,y_1)$ and an end point $(x_2,y_2)$ and radius of arc. How to calculate the co-ordinates of mid-poing of arc? The arc is the part of a circle.

Known Values

length of AD // that is radius
B(x,y)
C(x,y)


Needs to find

D(x,y)  // D is the mid-point of arc BC

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Well, if you know the coordinates of B and C, then you can find the midpoint M of the line segment BC, right? –  user5137 Jan 3 '12 at 19:57
Yes I can find the midpoint of BC line-segment. I am asking for BC arc! –  coure2011 Jan 3 '12 at 20:01
go to $(B-C)/2$ and move perpendicular a distance of $\sqrt{r^2-|B-C|^2/4}$ to get to a center of a circle of radius $r$ through $A,B$. or solve $(a_1-h)^2+(a_2-k)^2=r^2,(b_1-h)^2+(b_2-k)^2=r^2$ for a center $(h,k)$, where $A=(a_1,a_2),B=(b_1,b_2)$ –  yoyo Jan 3 '12 at 20:03
@coure2011 - There's no need to yell. You want help, right? Regardless, if you have the midpoint of the line segment BC, how can you use that to get the midpoint of the arc? –  user5137 Jan 3 '12 at 20:05