QJEEM19Ma43eb: JEE Main 2019 Mathematics - Class 11 JEEM19Ma43eb Solution: A rectangle is inscribed in a circle with a diameter lying…

Distance beetween point A and B is = 14 unit

As y coordinate of point A(-8, 5) and B(6, 5) are same. So line AB is parallel to the x axis.

Point O is the center of the circle and OP is the perpendicular to the line AB. And P is the mis point of line AB.

$\therefore$ Point P = $\left( {{{ - 8 + 6} \over 2},{{5 + 5} \over 2}} \right)$ = (-1, 5)

As OP is perpendicular to the line AB and AB is parallel to the x axis then OP is parallel to the y axis. So x coordinate of line OP is constant.

$\therefore$ x coordinate of O = -1

And point O is lies on the line 3y = x + 7

$\therefore$ 3y = -1 + 7

$\Rightarrow$ y = 2

$\therefore$ Center O = (-1, 2)

$\therefore$ OP = 3

Then BC = 2OP = 6

$\therefore$ Area of rectangle = (AB)(BC)

= 14 $\times$ 6

= 84