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Three circles all of radius 2 cm touch as shown in the diagram.
A straight line AG is tangential to the third circle, meeting the middle circle at H and I.
How long is HI?
What if there are four or more circles?
Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?
P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.