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Triangle Incircle Iteration

Keep constructing triangles in the incircle of the previous triangle. What happens?

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Lawnmower

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?

Circumspection

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

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).

Pick up a pencil, do some drawing, play with this. Look at angles APM, MPD, AEM, MCD and look for cyclic quadrilaterals. The proof that the lines AD and BE produced pass through P takes three or four lines.