SOLUTION: @Fombitz : I would like to email you but I can't since I don't know your email. Anyway, the setup was indeed exactly like I wanted , now I need some guidelines to solve this

Algebra ->  Points-lines-and-rays -> SOLUTION: @Fombitz : I would like to email you but I can't since I don't know your email. Anyway, the setup was indeed exactly like I wanted , now I need some guidelines to solve this      Log On


   



Question 878605: @Fombitz :
I would like to email you but I can't since I don't know your email.
Anyway, the setup was indeed exactly like I wanted , now I need some guidelines to solve this

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
OK great.
So let's find the angle that the line from point C to point B makes with the x-axis.
If we look at it like vector addition from (0,0), then
C+CB=B
CB=B-C
where C,B, and CB are vectors.
So then the components of CB are (x%5Bb%5D-x%5Bc%5D,y%5Bb%5D-y%5Bc%5D) and the angle theta would be calculated using,
tan%28theta%29=%28y%5Bb%5D-y%5Bc%5D%29%2F%28x%5Bb%5D-x%5Bc%5D%29 <--- Watch when you code this because you need to capture the exact angle since tan%28x%29=tan%28x%2Bpi%29
OK so that's the direction and now the distance.
Like I said before, it's the distance from C to B plus radius of B plus the radius of A.
So, the distance from C to B is,
D%5E2=%28x%5Bb%5D-x%5Bc%5D%29%5E2%2B%28y%5Bb%5D-y%5Bc%5D%29%5E2
D=sqrt%28%28x%5Bb%5D-x%5Bc%5D%29%5E2%2B%28y%5Bb%5D-y%5Bc%5D%29%5E2%29
So then the total distance is,
D%5Bmax%5D=D%2BR%5Bb%5D%2BR%5Ba%5D

So now you start at the origin, go to point C, and then apply the maximum distance and direction.
Breaking down the distance into x,y coordinates.
x%5Bmax%5D=D%5Bmax%5Dcos%28theta%29
y%5Bmax%5D=D%5Bmax%5Dsin%28theta%29
and finally,
x%5Ba%5D=x%5Bmax%5D%2Bx%5Bc%5D
y%5Ba%5D=y%5Bmax%5D%2By%5Bc%5D
You could also start from B.
x%5Ba%5D=x%5Bb%5D%2B%28R%5BA%5D%2BR%5BB%5D%29%2Acos%28theta%29
x%5Ba%5D=x%5Bb%5D%2B%28R%5BA%5D%2BR%5BB%5D%29%2Asin%28theta%29
If that's easier.
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Here's your example from before,
B : (10,20), R[B]=2
C : (15,25)
A : R[A]=3
CB : (-5,-5)
THETA: 225 degrees
D : 7.071
Dmax : 12.071
Dmax(x,y): (-8.53,-8.53)
A : (6.46,16.46)