MathDB

2

Part of 2001 Czech-Polish-Slovak Match

Problems(1)

Isosceles triangles constructed on the sides of a triangle

Source: Czech-Polish-Slovak 2001 Q2

4/30/2013
A triangle ABCABC has acute angles at AA and BB. Isosceles triangles ACDACD and BCEBCE with bases ACAC and BCBC are constructed externally to triangle ABCABC such that ∠ADC=∠ABC\angle ADC = \angle ABC and ∠BEC=∠BAC\angle BEC = \angle BAC. Let SS be the circumcenter of △ABC\triangle ABC. Prove that the length of the polygonal line DSEDSE equals the perimeter of triangle ABCABC if and only if ∠ACB\angle ACB is right.
geometrycircumcircleperimetergeometric transformationreflectionparallelogramgeometry unsolved