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The diagram shows two concentric circles and a regular hexagon. Two vertices of the hexagon lie on the smaller circle, and two on the larger circle. One vertex lies at the centre of the two circles.

What fraction of the larger circle is shaded?

Let the radius of the shaded circle be maths.

This is also the side length of the hexagon.

Area of shaded circle maths.

Join O B and AC where C is the midpoint of OB.

Maths equation since angle of a regular hexagon maths and mahts is isosceles.

In maths

Radius of the large circle maths

Area of large circle maths

maths of the large circle is shaded.

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