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Polish MO Finals 2018, Problem 5

Source:

April 19, 2018

geometryPolandradical axisgeometry solvedprojective geometryradical axes

Problem Statement

An acute triangle

ABC

in which

AB<AC

is given. Points

E

and

A

are feet of its heights from

EF

and

C

, respectively. The line tangent in point

A

to the circle escribed on

ABC

crosses

BC

at

P

. The line parallel to

BC

that goes through point

A

crosses

EF

at

Q

. Prove

PQ

is perpendicular to the median from

A

of triangle

ABC

.

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