Question

A rhombus is inscribed in the region common to the two circles $x^2+y^2-4x-12=0$ and $x^2+y^2+4x-12=0$ with two of its vertices on the line joining the centers of the circles. The area of the rhombus is

• A. $8\sqrt{3}$ sq. units
• B. $4\sqrt{3}$ sq. units
• C. $6\sqrt{3}$ sq. units
• D. $2\sqrt{3}$ sq. units

Answer 1

The correct option is A $8\sqrt{3}$ sq. units

The circles are with centers $(2,0)$ and $(-2,0)$ and readius is $4$
Therefore, the y-axis is their common chord.
$\Delta ABC$ is equilateral triangle. Hence,
Area of $ADBC=\frac{2\times \sqrt{3}}{4}(4{)}^2=8\sqrt{3}$