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computational in a pentagon ABCDE, AB=AE, AC=AD, <BAE=90^o , <ACB=<ADE=135^o

Source: 2018 Cono Sur Shortlist G3

August 25, 2021

equal anglesgeometrypentagonequal segments

Problem Statement

Consider the pentagon

ABCDE

such that

AB = AE = x

AC = AD = y

\angle BAE = 90^o

and

\angle ACB = \angle ADE = 135^o

. It is known that

C

and

D

are inside the triangle

BAE

. Determine the length of

CD

in terms of

x

and

y