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China TST 2001 circumcenter and incenter

Source: China TST 2001, problem 5

May 22, 2005
geometrycircumcircleincentergeometry solved

Problem Statement

In the equilateral △ABC\bigtriangleup ABC, DD is a point on side BCBC. O1O_1 and I1I_1 are the circumcenter and incenter of △ABD\bigtriangleup ABD respectively, and O2O_2 and I2I_2 are the circumcenter and incenter of △ADC\bigtriangleup ADC respectively. O1I1O_1I_1 intersects O2I2O_2I_2 at PP. Find the locus of point PP as DD moves along BCBC.
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