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

Engineering

Mathematics

A Circle

Question

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Let vertex C is (6,k) then centre of circle

$(- 1, \frac{5 + k}{2})$

It lies on diameter 3y = x + 7

$\Rightarrow 3 (\frac{5 + k}{2}) = - 1 + 7$

⇒ k =–1

So, AB = 14 and BC = 6

Area = 14 × 6 = 84