Circle 3 Question 2
2. 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
(2019 Main, 9 April II )
(a) 72
(b) 84
(c) 98
(d) 56
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Answer:
Correct Answer: 2. (b)
Solution:
- Given points are $(-8,5)$ and $(6,5)$ in which $y$-coordinate is same, i.e. these points lie on horizontal line $y=5$.
Let $(-8, \beta)$ and $(6, \beta)$ are the coordinates of the other vertices of rectangle as shown in the figure.
Since, the mid-point of line joining points $(-8,5)$ and $(6, \beta)$ lies on the line $3 y=x+7$.
$$ \begin{array}{lr} \therefore & 3 \frac{5+\beta}{2}=\frac{-8+6}{2}+7 \\ \Rightarrow & 15+3 \beta=-2+14 \\ \Rightarrow & 3 \beta=-3 \Rightarrow \beta=-1 \end{array} $$
Now, area of rectangle $=|-8-6| \times|\beta-5|$
$$ =14 \times 6=84 $$
