KVPY SA Exam 05-Nov-2017 Question Paper

Question : 9 of 80

Marks: +1, -0

Let AB be a line segment of length 2. Construct a semicircle S with AB as diameter. Let C be the midpoint of the arc AB. Construct another semicircle T external to the triangle ABC with chord AC as diameter. The area of the region inside the semicircle T but outside S is

$π/2$
$1/2$
$π/√2$
$1/√2$

Validate

Solution:

∠ ACB = 90°

AC = √2

Required area = Area of semicircle having AC as diameter – Area under arc OAC but outside triangle AOC

=1/2(π(√2/2)^2)-(π/4-1/2)

=π/4-π/4+1/2=1/2

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