Let $A,B,C$ lie on a straight line. $B$ is lying between $A$ and $C$. Consider all circles passing through $B$ and $C$. The point of contact of the tangents from $A$ to these circles lies on .....

We have to identify the locus not give its equation. I tried to make the diagram and apply some geometry, I found a cyclic quadrilateral with vertices : $A$, centre of circle and ends of chord of contact. But, I am unable to proceed further. Any help would be appreciated.


The locus will be a circle.
Let the point of contact from the tangent be $P$. Note that for any circle through $B$ and $C$, $AB \times AC $ is a constant which is equal to $AP^2$(The length of the tangent squared-Tangent Secant Theorem)

  • $\begingroup$ So elementary... Thank you. $\endgroup$ – evil999man Apr 4 '14 at 4:26

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.