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Quad in Quad

The points P, Q, R and S are the midpoints of the edges of a convex quadrilateral. What do you notice about the quadrilateral PQRS as the convex quadrilateral changes?

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Matter of Scale

Prove Pythagoras' Theorem using enlargements and scale factors.

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Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. What is the value of r/R?

Similar Rectangles

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The smaller of two similar rectangles has height $2$ units; the larger rectangle has length $6$ units.

If one rectangle has twice the area of the other, find the length of the smaller rectangle.

This problem is taken from Tony Gardiner's 'Extension Mathematics Gamma' book.