If the circular arcs $AC$ and $BC$ have centres at $B(-\alpha, 0) $and $A(\alpha, 0)$ respectively and the length of the arc BC is $8\pi$ . Find the equation of the circle which touches both arcs $AC$ and $BC$ and the line $AB$.

The major problem I am facing is that I am not able to figure out what kind of diagram will be made in this case i.e. I am not able to determine how the diagram would look like. Any help over the problem is appreciated.

  • $\begingroup$ Where did you receive this interesting question? $\endgroup$ Dec 25, 2017 at 17:12
  • $\begingroup$ Are AC and BC equal? $\endgroup$ Dec 25, 2017 at 17:43
  • $\begingroup$ I guess so. But I am not quite sure. $\endgroup$ Dec 25, 2017 at 17:44

1 Answer 1


I hope this picture will help you to figure out better how to solve analytically the problem.

Hope it helps


enter image description here

  • $\begingroup$ Thanks a lot for your help. $\endgroup$ Dec 25, 2017 at 18:55

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