There are two concentric circles. The radius of the outer circle is 8.5 cm and the length of the longest chord of the outer circle that doesn’t cut through the inner circle is 8 cm. what fraction of the bigger circle is not covered by the smaller circle?

Options
- 64/289
- 8/17
- 225/289
- 89/289

CORRECT ANSWER : 64/289

Discussion Board
Solution

The longest chord of the outer circle that doesn''t cut through the inner circle will be the tangent to the inner circle.
Then we get two sides of the right angled triangle with the half of the chord, inner circle radius and the outer circle radius as the sides.
Using pythogoras theorem, we get inner radius
R^2 = r^2 + 4^2
R^2 - r^2 = 16

Since, fraction of the bigger circle not covered by smaller
= (Bigger area - Smaller area) /Bigger area
= (R^2 - r^2) /R^2
= 16/72.25
i.e, 64/289




Ganesh Banoth 09-3-2021 03:55 PM

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