A circle \( C \) touches the line \( x = 2y \) at the point \( (2, 1) \) and intersects the circle \( C_1 : x^2 + y^2 + 2y - 5 = 0 \) at two points \( P \) and \( Q \) such that \( PQ \) is a diameter of \( C_1 \). Then the diameter of \( C \) is:
\( 15 \)
\( 7\sqrt{5} \)
\( 4\sqrt{15} \)
\( \sqrt{285} \)
