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Part of 2004 Tournament Of Towns

Problems(2)

Source: Tournament of Towns, Junior A-level paper, Fall 2004

Let A and B be two rectangles such that it is possible to get rectangle similar to A by putting together rectangles equal to B. Show that it is possible to get rectangle similar to B by putting together rectangles equal to A.

geometryrectanglecombinatorics unsolvedcombinatorics

Angles identified by a rotation of the plane

Source: Tournament of towns, Senior A-Level paper, Fall 2004

Let AOB and COD be angles which can be identified by a rotation of the plane (such that rays OA and OC are identified). A circle is inscribed in each of these angles; these circles intersect at points E and F. Show that angles AOE and DOF are equal.

geometrygeometric transformationrotationgeometry solved