KVPY SA Exam 05-Nov-2017 Question Paper

Question : 14 of 80

Marks: +1, -0

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

${9-π}/6$
${8-π}/6$
${7-π}/7$
${6-π}/4$

Validate

Solution:

∴ ∠OAC = 90° as AC is tangent and OA is radius
as ∠CAD = 45°
So ∠OAD = 45°= ∠AOD
∴

OA=√2

Area of shaded region
= 1 – (area of sector OAX – area of ∆OAD)

=1-[1/2×2×π/4-1/2]

1-[π/4-1/2]=3/2-π/4

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