If a line, y = mx + c is a tangent to the circle, (x – 3)² + y² = 1 and it is perpendicular to a line L₁, where L₁ is the tangent to the circle, x² + y² = 1 at the point $$\left( {{1 \over {\sqrt 2 }},{1 \over {\sqrt 2 }}} \right)$$, then :

Let the tangents drawn from the origin to the circle,
x² + y² - 8x - 4y + 16 = 0 touch it at the points A and B. The (AB)² is equal to :

A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point :

If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90^o, then the length (in cm) of their common chord is :