MathDB

2016.8.51

Part of Kyiv City MO Juniors 2003+ geometry

Problems(1)

AX = AD if <BAX=<CDA,<ABC = <BCD, 2AB = CD (2016 Kyiv City MO 8.5.1)

Source:

9/5/2020
In the quadrilateral ABCDABCD, shown in fig. , the equations are true: ∠ABC=∠BCD\angle ABC = \angle BCD and 2AB=CD2AB = CD. On the side BCBC, a point XX is selected such that ∠BAX=∠CDA\angle BAX = \angle CDA. Prove that AX=ADAX = AD. https://cdn.artofproblemsolving.com/attachments/2/9/0884eb311d1e40300c1e5980fd53eaadfa7a25.png
geometryequal anglesequal segments