The first two pages of this article present eight tricks, identified by subheadings, and eleven problems that use them. Take the time to look for each solution, using the suggested hints if necessary, before discovering it in the following two pages.
Be inventive
-------------
1- *A triangle ABC has base BC = 8 cm and area 12 cm2. There is a whole family of triangles with the same base [BC] and the same area.*
What is the minimum possible perimeter of such a triangle?
The first idea is to characterize the locus of A geometrically. The second is to turn the question into a search for a minimum distance, enabling us to locate A within this locus. This problem is related to finding the shortest route from one point to another while stopping for water on the bank of a straight river.
