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ratio, lines symmetric wrt line (IV Soros Olympiad 1997-98 Correspondence 10.8)

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June 1, 2024

ratiogeometry

Problem Statement

In triangle

ABC

, angle

B

is different from a right angle,

AB : BC = k

. Let

M

be the midpoint of

AC

. Lines symmetric to

BM

wrt

AB

and

BC

intersect line

AC

at points

D

and

E

. Find

BD : BE

.

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