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Albania IMO TST Geometry

Source:

May 19, 2013

geometryratiocircumcirclegeometry proposed

Problem Statement

It is given an acute triangle

ABC

,

AB \neq AC

where the feet of altitude from

A

its

H

. In the extensions of the sides

AB

and

AC

(in the direction of

B

and

C

) we take the points

P

and

Q

respectively such that

HP=HQ

and the points

B,C,P,Q

are concyclic. Find the ratio

\tfrac{HP}{HA}

.

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