MathDB

If these ratios are equal, then the points are concyclic

Source: Czech-Polish-Slovak 2002 Q5

April 28, 2013

ratiogeometrycircumcirclegeometric transformationgeometry unsolved

Problem Statement

In an acute-angled triangle

ABC

with circumcenter

O

, points

P

and

Q

are taken on sides

AC

and

BC

respectively such that

\frac{AP}{PQ} = \frac{BC}{AB}

and

\frac{BQ}{PQ} =\frac{AC}{AB}

. Prove that the points

O, P,Q,C

lie on a circle.