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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 : 
  1. 56
  2. 98
  3. 72
  4. 84


Solution

The correct option is D 84
Let the coordinates of point C be (6,K)
Centre of circle will be the midpoint of line AC
Coordinates of centre 0 is (1,K+52)
Centre lies on 3y=x+7
3(K+52)=6K=1
AB=14 units and BC=6 units
Area of rectangle=84 sq. units

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