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AB/BC wanted, MD_|_BD, angle bisector, midpoint related

Source: 2006 Argentina OMA L3 p2

June 16, 2020

geometryangle bisectorperpendicularratio

Problem Statement

In triangle

ABC, M

is the midpoint of

AB

and

D

the foot of the bisector of angle

\angle ABC

. If

MD

and

BD

are known to be perpendicular, calculate

\frac{AB}{BC}