Question:
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 :
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 :
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The center lies on the perpendicular bisector of the given side and on the given diameter line.
Updated On: Nov 5, 2026
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The Correct Option is B
Solution and Explanation
The side joining \((-8,5)\) and \((6,5)\) is horizontal with length \(14\).
The center of the rectangle lies on the perpendicular bisector \(x = \frac{-8+6}{2} = -1\).
A diameter passes through the center, so center lies on \(3y = x+7\): \(3y = -1 + 7 = 6 \Rightarrow y=2\). Center \(=(-1,2)\).
The other side is at distance \(2(5-2) = 6\) from the given side (vertical extent).
Area \(= 14\times6 = 84\).
Answer: (2) 84
The center of the rectangle lies on the perpendicular bisector \(x = \frac{-8+6}{2} = -1\).
A diameter passes through the center, so center lies on \(3y = x+7\): \(3y = -1 + 7 = 6 \Rightarrow y=2\). Center \(=(-1,2)\).
The other side is at distance \(2(5-2) = 6\) from the given side (vertical extent).
Area \(= 14\times6 = 84\).
Answer: (2) 84
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