There are three circles, all of them touching each other. The bottom two circles are laying on an imaginary floor, such that they touch the line g=-r as well.
Given are all three radii, r1 (A), r2 (B) and r3 (C).
Assuming circle A has its center on (0/0), B has its center on (2 sqrt(r1 * r2), r2 – r1). I am now supposed to find the coordinates of C.
Is this a know problem and has an easy/straighforward solution? I can't seem to find a nice approach.
Best Answer
Since you know the radii $r_1$, $r_2$, and $r_3$ and the centers $A$ and $B$, the center $C(x_c,y_c)$ must be a distance $r_1+r_3$ from $A$ and a distance $r_2+r_3$ from $B$, which gives the two equations $$x_c^2+y_c^2=(r_1+r_3)^2$$ and $$(x_c-2\sqrt{r_1r_2})^2+(y_c-(r_2-r_1))^2=(r_2+r_3)^2$$ Solving the system for $(x_c,y_c)$ should give the two possible coordinate pairs for $C$ (one as you've pictured, the other "below" the first two circles).