MathDB

Albanian IMO TST 2010 Question 1

Source:

May 22, 2010

ratiogeometrycircumcircleparallelogramincenterrhombusgeometry unsolved

Problem Statement

ABC

is an acute angle triangle such that

AB>AC

and

\hat{BAC}=60^{\circ}

. Let's denote by

O

the center of the circumscribed circle of the triangle and

H

the intersection of altitudes of this triangle. Line

OH

intersects

AB

in point

P

and

AC

in point

Q

. Find the value of the ration

\frac{PO}{HQ}