A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C1 : x2 + y2 + 2y $-$ 5 = 0 at two points P and Q such that PQ is a diameter of C1. Then the diameter of C is :

Question

A circle C touches the line x = 2y at the point (2, 1) and intersects the circle

C₁ : x² + y² + 2y $-$ 5 = 0 at two points P and Q such that PQ is a diameter of C₁. Then the diameter of C is :

$7\sqrt 5 $