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ratio chasing, AB/BC=AC/CD=l -- VI Soros Olympiad 1999-00 Round 1 9.7

Source:

May 21, 2024

ratiogeometry

Problem Statement

Points

A, B, C

and

D

are located on line

\ell

so that

\frac{AB}{BC}=\frac{AC}{CD}=\lambda

. A certain circle is tangent to line

\ell

at point

C

. A line is drawn through

A

that intersects this circle at points

M

and

N

such that the bisector perpendiculars to segments

BM

and

DN

intersect at point

Q

on line

\ell

. In what ratio does point

Q

divide segment

AD

?

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