JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
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 \(72\)
- B \(84\)
- C \(98\)
- D \(56\)
Answer & Solution
Correct Answer
(B) \(84\)
Step-by-step Solution
Detailed explanation
Let vertex \(C\) is \(\left( {6,k} \right)\) then centre of circle \(\left( { - 1,\frac{{5 + k}}{2}} \right)\) It lies on diamenter \(3y = x + 7\) \( \Rightarrow 3\left( {\frac{{5 + k}}{2}} \right) = - 1 + 7\) \( \Rightarrow k = - 1\) So, \(AB = 14\) and \(BC = 6\) Area…
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