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Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

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From All Corners

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

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Star Gazing

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

Triangle in a Triangle

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

An outstanding solution, taking full advantage of the power of vectors was sent in by Steven from Sunderland College. The solution was so neatly presented that we link directly to it here .