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Grade 8

The circle in the gap

Four equal circles leave a gap in the middle, and the circle that fills it is smaller than it looks. The skill is drawing the square the four centres make -- Pythagoras does the rest.

  1. 1

    Shaded area

    1 cm
    Four identical circles, each of radius 1 cm, are arranged in a square, each one touching the two beside it. A smaller circle fits snugly in the gap between them, touching all four. What is the area of the circle in the gap?