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trapezoid ABCD, AB = 70, AD = 32 , BC = 49, <ABC = 3 <ADC

Source: 2021 Dürer Math Competition Finals Day2 E13 https://artofproblemsolving.com/community/c2749870

January 8, 2022
geometrytrapezoidequal angles

Problem Statement

The trapezoid ABCDABCD satisfies AB∥CDAB \parallel CD, AB=70AB = 70, AD=32AD = 32 and BC=49BC = 49. We also know that ∠ABC=3∠ADC\angle ABC = 3 \angle ADC. How long is the base CDCD?
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