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  • 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)

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

Option: 1

84


Option: 2

86


Option: 3

88


Option: 4

80


Answers (1)

best_answer

Let the vertices of the rectangle are A(–8, 5), B(6, 5), \mathrm{C(6, \alpha) \text { and } D(-8, \beta)}. So, coordinates of mid point of diameter

\mathrm{A C \text { are }\left(\frac{-8+6}{2}, \frac{\alpha+5}{2}\right)=\left(-1, \frac{\alpha+5}{2}\right)}

It lies on the line, 3y = x + 7

\mathrm{\begin{aligned} & \Rightarrow 3\left(\frac{\alpha+5}{2}\right)=-1+7 \\ & \Rightarrow \alpha+5=\frac{6 \times 2}{3} \Rightarrow \alpha=-1 \end{aligned}}

\mathrm{\text { Now, } A B=\sqrt{(-8-6)^2+0}=14}

\mathrm{B C=\sqrt{0+(5+1)^2}=6}

Sides of rectangle are 14 and 6.
Hence, area of rectangle = 14 × 6 = 84 sq. units.

Posted by

HARSH KANKARIA

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