Multiple choice

AB is chord of the circle $x^2+y^2=25$. The tangents of A and B intersect at C. If $(2,3)$ is the mid-point of AB, then area of the quadrilateral OACB is

  1. $50\sqrt { \frac { 13 }{ 3 } } $
  2. $50\sqrt { \frac { 3 }{ 13 } } $
  3. $50\sqrt3$
  4. $\dfrac{50}{\sqrt3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The chord AB has midpoint (2,3). The line from the origin to the midpoint is perpendicular to the chord. The area of quadrilateral OACB is 2 * Area(triangle OAC). Area(OAC) = 1/2 * base * height. This is a standard geometry problem for a circle.

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