Multiple choice

In the accompanying figure, AB is one of the diameters of he circle and OC is perpendicular to it through the center O. If AC is $7\sqrt 2$ cm, then what is the area of the circle in sq.cm?

  1. 24.5

  2. 49

  3. 98

  4. 154
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D Correct answer
Explanation

Since OC is perpendicular to diameter AB through the center, triangle AOC is right-angled with OA = OC = r. Therefore, AC = r√2, so r = 7 cm. The area is pi r^2 = 154 cm^2 using pi = 22/7.

AI explanation

Since OC is perpendicular to diameter AB through center O, triangle AOC is a right isosceles triangle with OA = OC = r. Using the Pythagorean theorem, we have r squared plus r squared equals the square of AC, so 2r squared equals the square of 7 root 2, which is 98. This gives r squared as 49, meaning the radius is 7 cm. The area of the circle is pi times r squared, which is 22/7 times 49, yielding 154 sq. cm.

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