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JEE Main202227 Jun 2022Morning ShiftMathematicsCircleActual

A rectangle R with end points of the one of its sides as 1 , 2 and 3 , 6 is inscribed in a circle. If the equation of a diameter of the circle is 2 x - y + 4 = 0 , then the area of R is _____.

Correct answer

0

Step-by-step solution

Equation of line A B will be y - 2 = 2 x - 1 ⇒ 2 x - y = 0 Now the given diameter is parallel to A B Then, the distance between diameter and line A B = 4 2 2 + 1 2 = 4 5 Thus, B C = 2 × 4 5 = 8 5 Also A B = 1 - 3 2 + 2 - 6 2 = 20 = 2 5 Area of the rectangle = A B × B C = 8 5 × 2 5 = 16

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