Let the circle \( S: 36x^2 + 36y^2 - 108x + 120y + c = 0 \) be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, \( x - 2y = 4 \) and \( 2x - y = 5 \) lies inside the circle \( S \), then:
\( 100 < c < 165 \)
\( \dfrac{25}{9} < c < \dfrac{13}{3} \)
\( 100 < c < 156 \)
\( 81 < c < 156 \)
