Question

A rectangle is inscribed in a circle with a diameter lying along the line $3y=x+7$. If the two adjacent vertices of the rectangle are $(-8,5)$ and $(6,5)$, then the area of the rectangle (in sq. units) is :

• A. $56$
• B. $72$
• C. $84$
• D. $98$

Answer 1

The correct option is C $84$



Let the coordinates of point $C$ be $(6,K).$
Centre of circle will be the midpoint of line $AC.$
Coordinates of centre $O$ is $(-1,\frac{K+5}{2})$
Centre lies on $3y=x+7$
$\therefore 3\left(\frac{K+5}{2}\right)=6\Rightarrow K=-1$
$\therefore AB=14$ units and $BC=6$ units
Area of rectangle $=84$ sq. units