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D is an interior point of segment AE

Source: MEMO 2008, Team, Problem 7

September 10, 2008

geometry unsolvedgeometry

Problem Statement

Let

ABC

be an acute-angled triangle. Let

E

be a point such

E

and

B

are on distinct sides of the line

AC,

and

D

is an interior point of segment

AE.

We have \angle ADB \equal{} \angle CDE, \angle BAD \equal{} \angle ECD, and \angle ACB \equal{} \angle EBA. Prove that

B, C

and

E

lie on the same line.