0
$\begingroup$

Find the locus of centre of all circles which are of given radius and touch a given circle. I can make out that it is a circle but I am unable to prove it.

$\endgroup$
  • 2
    $\begingroup$ I think that the locus is again a circle of some certain radius $\sqrt {a^2+b^2+r^2 - s^2}$ where $(a,b)$ is the centre of the given circle with radius $s$ and $r$ is the given radius of the circles whose locus of centres has to be determined. $\endgroup$ – Dbchatto67 Mar 20 at 5:14
0
$\begingroup$

Consider a given circle $S^1$ have center (a,b) and radius $r_1$. Let the varying circle with center $(x, y)$ and constant radius $r_2$touches $S^1$. Since the circles touches each other the distance between their centers is constant , $r_1+r_2$.

Thus equating the distance gives $$(x-a)^2+( y-b)^2=(r_1+r_2)^2.$$Which is an equation of a circle centered at $(a,b)$ and radius $(r_1+r_2)$. Thus the locus $(x,y)$ forms a circle.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.