A circle of unit radius touches the positive x and y axes. Two parallel tangents A B and D C having slopes - 1 are drawn to the circle cutting x -axis at B and C and y -axis at A and D respectively. The square of the area of the trapezium A B C D is equal to

Question

A circle of unit radius touches the positive x and y axes. Two parallel tangents A B and D C having slopes - 1 are drawn to the circle cutting x -axis at B and C and y -axis at A and D respectively. The square of the area of the trapezium A B C D is equal to,

MARKS App · Accepted Answer

Let the tangent line be x + y = c Now, | 1 + 1 - c | 2 = 1 ⇒ c = 2 ± 2 ∴ A 0,2 + 2 , B 2 + 2 , 0 C 2 - 2 , 0 , D 0,2 - 2 So, the area of the trapezium A B C D = 1 2 2 2 2 + 2 + 2 · 2 - 2 = 4 2 sq. units Hence, the square of the area = 4 2 2 = 32

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