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Q. In the figure, ABCD is a unit square. A circle is drawn with centre O on the extended line CD and passing through A. If the diagonal AC is tangent to the circle, then the area of the shaded region is
image

KVPYKVPY 2017

Solution:

Given, ABCD is a square
AB=CD=AD=BC=1
AC is tangent of circle
OAC=90
CAD=45
OAD=45
OA=2
image
Area of shaded region
=Area of square + Area of ΔAOD Area of sector
=1+12×145360×(2)2π
=1+12π4=32π4=6π4