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Circle question

2019 · Shift 1 · Q32
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  5. /2019 · Shift 1 · Q32

Circle question

2019 · Shift 1 · Q32

JEE AdvancedMathematicsCircleNumerical+3 / −1
Let the point B be the reflection of the point A(2, 3) with respect to the line 8x−6y−23=08x - 6y - 23 = 08x−6y−23=0. Let ΓA\Gamma_{A}ΓA​ and ΓB\Gamma_{B}ΓB​ be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles ΓA\Gamma_{A}ΓA​ and ΓB\Gamma_{B}ΓB​ 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 .................
Numerical answer
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