Question

if an external point of a circle is at a distance equal to the diameter of the circle from the center of the circle, the length of the tangent drawn from the external point is?

Answer 1

Let the radius of the circle be r. Then the line from the external point through the center of the circle which extends to the far point on the circle has length 3r .By the tangent - secant theorem

t^2 = 3r * r = 3r^2 ( where t is the length of the tangent).

So t = √(3r^2) = √3r answer.