MathDB

11

Part of 2007 Baltic Way

Problems(1)

S must be the incentre of triangle ABC

Source: Baltic Way 2007

11/30/2010
In triangle ABCABC let AD,BEAD,BE and CFCF be the altitudes. Let the points P,Q,RP,Q,R and SS fulfil the following requirements: i) PP is the circumcentre of triangle ABCABC. ii) All the segments PQ,QRPQ,QR and RSRS are equal to the circumradius of triangle ABCABC. iii) The oriented segment PQPQ has the same direction as the oriented segment ADAD. Similarly, QRQR has the same direction as BEBE, and RsRs has the same direction as CFCF. Prove that SS is the incentre of triangle ABCABC.
geometryincentercircumcircletrigonometrygeometry proposed