MathDB

5

Part of 2002 Czech-Polish-Slovak Match

Problems(1)

If these ratios are equal, then the points are concyclic

Source: Czech-Polish-Slovak 2002 Q5

4/28/2013
In an acute-angled triangle ABCABC with circumcenter OO, points PP and QQ are taken on sides ACAC and BCBC respectively such that APPQ=BCAB\frac{AP}{PQ} = \frac{BC}{AB} and BQPQ=ACAB\frac{BQ}{PQ} =\frac{AC}{AB} . Prove that the points O,P,Q,CO, P,Q,C lie on a circle.
ratiogeometrycircumcirclegeometric transformationgeometry unsolved