Brilliant Gamees - Quarter Quell 4

Geometry Level 1

In the above figure of 2 overlapping circles, the area of the overlapped region is 1 4 \frac{1}{4} of the small circle's area, and 1 5 \frac{1}{5} of the large circle's area.

What is the ratio of the area of the large circle to the small circle?

6:5 4:3 5:4 3:2

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2 solutions

Sharky Kesa
Mar 10, 2015

Assume that the overlapped region had an area of x x . Then, the large circle has an area of 5 x 5x and the small circle has an area of 4 x 4x . The ratio of their areas would be 5 : 4 5:4 .

Yay, it's that simple.

Chung Kevin - 6 years, 3 months ago
Gamal Sultan
Mar 17, 2015

Let the areas of the small and large circles be x, y respectively

Then

1/4 x =1/5 y

y/x = 5/4

y : x = 5 : 4

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