Multiple choice

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

  1. $\dfrac{32}{5}$
  2. $\dfrac{56}{5}$
  3. $\dfrac{52}{5}$
  4. $\dfrac{64}{5}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The length of the chord of contact AB is given by 2*r*d / sqrt(r^2 + d^2), where r is the radius and d is the distance from the origin to the center. Here center is (4,2), r=2, d=sqrt(20). Calculation leads to 64/5.

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