ARC AB of length 5 cm subtends an angle of 45 degrees at the center of the circle. Chord MN of length 9 cm subtends an angle of 90 degree at the centre of the circle.
Each statement alone is sufficient- (ans: (d) area of the circle = pi (r^2), where r is the radius of circle.
take (1), length of arc = 2 pi r (angle subtended by the arc) / 360
or 5 = 2 pi r (45)/360 or pi r = 20 or r = 20 x 7 / 22
with this value of radius r, we can find the area of the circle, so (1) is sufficient.
now take (2), since chord subtends a right angle, so using pythagoras theorem
we get, 9^2 = r^2 + r^2 or r = 9/square root (2)
with this value of radius r, we can find the area of the circle, so (2) is also sufficient
hence both (1) & (2) are independently sufficient, hence (d) is the answer.)
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