MathDB

3

Part of 2021 Grand Duchy of Lithuania

Problems(1)

right triangle from AC,BD,CD if <ADB + <ACB = <CAB + <DBA = 30^o, AD = BC.

Source: 2021 Grand Duchy of Lithuania, Mathematical Contest p3 (Baltic Way TST) https://artofproblemsolving.com/community/c1321893_grand

10/30/2021
Let ABCDABCD be a convex quadrilateral satisfying ∠ADB+∠ACB=∠CAB+∠DBA=30o\angle ADB + \angle ACB = \angle CAB + \angle DBA = 30^o, AD=BCAD = BC. Prove that there exists a right-angled triangle with side lengths ACAC, BDBD, CDCD.
geometryright triangleangles