MathDB

4

Part of 1963 German National Olympiad

Problems(1)

octagon with equal sides by removing 4 right triangles from a rectangle

Source: 1962-63 Germany R4 12.4 https://artofproblemsolving.com/community/c3208025_

10/12/2024
Consider a rectangle with sides 2a2a and 2b2b, where a>ba > b. There should be four congruent right triangles (one triangle at each vertex of this rectangle , whose legs are on the sides of the rectangle lie) must be cut off so that the remaining figure forms an octagon with sides of equal length. The side of the octagon is to be expressed in terms of a and bb and constructed from aa and bb. Besides that it must be stated under which conditions the problem can be solved.
geometryoctagonrectangle