SATHEE: Circle 3 Question 2

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

(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 $(- 8, β)$ and $(6, β)$ 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 $(6, β)$ lies on the line $3 y = x + 7$ .

$\begin{array}{lr} ∴ & 3 \frac{5 + β}{2} = \frac{- 8 + 6}{2} + 7 \\ \Rightarrow & 15 + 3 β = - 2 + 14 \\ \Rightarrow & 3 β = - 3 \Rightarrow β = - 1 \end{array}$

Now, area of rectangle $= | - 8 - 6 | \times | β - 5 |$

$= 14 \times 6 = 84$

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Circle 3 Question 2

2. A rectangle is inscribed in a circle with a diameter lying along the line 3y=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

Answer:

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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