let the point B be the reflection of the point A(2,3) with respect to the line 8x-6y-23=0. let `T_(A)` and `T_(B)` be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles `T_(A)` and `T_(B)` such that both the circles are on the same side of `T`. if C is the point of intersection of T and the line passing through A and B then the length of the line segment AC is

Answer

10

Explanation

`AL=|(16-18-23)/(10)|=(5)/(2)`
`(CB)/(CA)=(1)/(2)`
`(CA-5)/(CA)=(1)/(2)`
`CA=10`