# Intersection between two circles (3)

### Given O1(x1,y1,z1), O2(x2,y2,z2), the center of the circles and r1 and r2,
their Radius

### Given M(x,y,z) the intersection, then another way is ...

###
O1H = x

### MH = h

### 0102 = d

### H02 = d - x

### (1) R12
= h2 + x2

### (2) R22
= h2 + (d - x )2
= h2 + d2 -2dx +
x2

### (2) - (1) R22
- R12 = d2
- 2dx

### => x = (d2
- R22 + R12)/2d

### (1) h = +/- squareroot(R12
- x2)

## M = O1 + O1
H +/- HM

Then O1H = x. O1O2/||O1O2||
then inverse -x and y of O1O2/||O1O2|| vector to get an orthogonal vector