# Math Help - circular towers of unequal radii

1. ## circular towers of unequal radii

Suppose that you stand on an infinite plane upon which are two circular towers of unequal radii. The apparent width of each tower is the angle subtended where you stand. Show that the locus of points from which both towers appear to be equally wide is a circle.

2. Originally Posted by scipa
Suppose that you stand on an infinite plane upon which are two circular towers of unequal radii. The apparent width of each tower is the angle subtended where you stand. Show that the locus of points from which both towers appear to be equally wide is a circle.
The locus is the curve such that the ratio of the distances of the centres of the two towers from a point on the locus is a constant, equal to the ratio of the towers radii.

Will get back to this if you are still having trouble.

RonL

3. thanks - funny that I didn't see that!

so, giving the centers of the 2 circles the coordinates (x_1,0) and (x_2,0) with radii r_1 and r_2, respectively, I've ended up with the attached (since LaTeX doesn't seem to be working) equation for the curve:

4. Originally Posted by scipa
thanks - funny that I didn't see that!

so, giving the centers of the 2 circles the coordinates (x_1,0) and (x_2,0) with radii r_1 and r_2, respectively, I've ended up with the attached (since LaTeX doesn't seem to be working) equation for the curve:
Which is a circle as it is of the form:

y^2+(x-c)^2 = r^2

which has centre $(c,0)$ and radius $r$

RonL