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# Round and Round

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### Percentage Unchanged

### Circle Packing

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Age 14 to 16

Challenge Level

Prove that the shaded area of the semicircle is equal to the area of the inner circle.

What percentage of the sector OAB is taken up with the inner circle?

What happens if angle AOB is less than 90 ° or between 90 and 180 degrees?

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ?

Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...