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### Number and algebra

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# 2D-3D

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Age 16 to 18

Challenge Level

- Problem
- Student Solutions

Two circles of equal size intersect and the centre of each circle is on the circumference of the other.

What is the area of the intersection?

Now imagine that the diagram represents two spheres of equal volume with the centre of each sphere on the surface of the other.

What is the volume of intersection?

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.