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Q.

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

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a

98

b

84

c

56

d

72

answer is B.

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Detailed Solution

detailed_solution_thumbnail

Let ABCD be the rectangle

Let $A = (- 8, 5) & B = (6, 5)$

Let centre $= (- 1, α)$ lies on $3 y = x + 7$

Question Image

$3 α = 6$

$α = 2$

$∴ Centre = (- 1, 2)$

$A D = B C = 6$

$A B = 14$

Area of rectangle $= A B \times B C = 14 \times 6 = 84$

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