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When drawing trees with 7 vertices, you might find it helpful to start by working out what the sum of the degrees of the 7 vertices must be.
A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?