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Isotomic conjugates [intersections of median & incircle]

Source: belgian IMO preparation; IMO Shortlist 2005 geometry problem G6

March 25, 2006

geometryhomothetyreflectiontrapezoidIMO Shortlistprojective geometryPolars

Problem Statement

Let

\gamma

be a triangle, and

M

the midpoint of its side

BC

. Let

\gamma

be the incircle of triangle

ABC

. The median

AM

of triangle

ABC

intersects the incircle

\gamma

at two points

K

and

L

. Let the lines passing through

K

and

L

, parallel to

BC

, intersect the incircle

\gamma

again in two points

X

and

Y

. Let the lines

AX

and

AY

intersect

BC

again at the points

P

and

Q

. Prove that

BP = CQ

.

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