Question

From a point A which is at a distance of 10 cm from the center O of a circle of radius 6 cm, the pair of tangents AB and AC to the circle are drawn. Then the area of Quadrilateral ABOC is:

• A. $24c{m}^2$
• B. $48c{m}^2$
• C. $96c{m}^2$
• D. $100c{m}^2$

Answer 1

The correct option is B $48c{m}^2$

Since $△ABO$ is congruent to $△ACO$, area of $ABOC$ is twice the area of $△ABO$.

In $△ABO,OA=10cm,OB=6cm$.

Since tangent is perpendicular to radius at the point of contact, by Pythagoras' theorem, we have

$AB=\sqrt{O{A}^2-O{B}^2}=8cm$

So, the area of $△ABO$ is $\frac{1}{2}\times AB\times OB=24c{m}^2$

So, the area of $ABOC$ is $2\times 24=48c{m}^2$.

So option B is the right answer.