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)