One of the diameter of the circle circumscribing the rectangle $A B C D, 4 y=x+7$. If $A$ and $B$ ar

Question

One of the diameter of the circle circumscribing the rectangle $A B C D, 4 y=x+7$. If $A$ and $B$ are the points $(-3,4)$, and $(5,4)$ respectively, then find the area of the rectangle.

Professor PC Thomas Classes · Answer

Let $E$ be the midpoint of $A B$\ \ $E=(1,0)$\ Let $O$ be the centre of the circle.\ $A B$ is parallel to the $x$-axis.\ $	herefore \quad E O$ is parallel to the $y$-axis.\ $	herefore \quad$ Equation of $E O$ is equal to $x=1$\ Since the centre $O$ lies on $4 y=x+7$\ $4 y=1+7 \quad 	herefore y=2$\ $	herefore \quad$ centre is $(1,2), O E=2$.\ $	herefore \quad B C=4, A B=8$\ Area of the rectangle $A B C D=A B 	imes B C$ $=8 	imes 4=32$ sq. units.\