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M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.

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A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of grass exactly one foot wide and wishes to cut the entire lawn in parallel strips. What is the minimum number of strips the gardener must mow?

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Long Short

What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?

Triangle Incircle Iteration

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

Have you noticed that, whatever triangle you start with, the nested triangles get more and more like equilateral triangles? In fact this convergence is very rapid.

The question tells you how to show why this happens by considering iterative sequences.