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In the given figure ABCD is a rectangle. A quarter circle with centre at B is drawn such that side DC is tangent to it. A circle with radius r is inscribed in the rectangle such that it touches the three sides and the inscribed quarter circle. What is the area of ABCD?
  • a)
    8r2
  • b)
    2(1+2√2)r2
  • c)
    2(√3 + 2)r2
  • d)
    2(√3 - 2)r2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In the given figure ABCD is a rectangle. A quarter circle with centre...
Consider the figure shown below. As can be clearly seen from the figure, the line joining the centres of any two circles passes through the point of contact.
Note that the Diameter AD = 2r of smaller circle is the radius BC of the larger circle
So FB = r + 2r = 3r,then by Pythagoras theorem
and
Hence required area
=
Thus the correct option is 2
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In the given figure ABCD is a rectangle. A quarter circle with centre at B is drawn such that side DC is tangent to it. A circle with radius r is inscribed in the rectangle such that it touches the three sides and the inscribed quarter circle. What is the area of ABCD?a)8r2b)2(1+2√2)r2c)2(√3 + 2)r2d)2(√3 - 2)r2Correct answer is option 'B'. Can you explain this answer?
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