MathDB

6

Part of 1994 Turkey MO (2nd round)

Problems(1)

Turkish MO 1994 P6

Source: Turkish Mathematical Olympiad 2nd Round 1994

9/27/2006
The incircle of triangle ABCABC touches BCBC at DD and ACAC at EE. Let KK be the point on CBCB with CK=BDCK=BD, and LL be the point on CACA with AE=CLAE=CL. Lines AKAK and BLBL meet at PP. If QQ is the midpoint of BCBC, II the incenter, and GG the centroid of △ABC\triangle ABC, show that:
(a)(a) IQIQ and AKAK are parallel,
(b)(b) the triangles AIGAIG and QPGQPG have equal area.
geometryincenterperimetertrigonometrytrapezoidangle bisectorgeometry unsolved