MathDB

2

Part of 2008 Costa Rica - Final Round

Problems(1)

Costa Rican math olympiad 2008 Problem 2

Source:

6/18/2009
Let ABC ABC be a triangle and let P P be a point on the angle bisector AD AD, with D D on BC BC. Let E E, F F and G G be the intersections of AP AP, BP BP and CP CP with the circumcircle of the triangle, respectively. Let H H be the intersection of EF EF and AC AC, and let I I be the intersection of EG EG and AB AB. Determine the geometric place of the intersection of BH BH and CI CI when P P varies.
geometrycircumcircleprojective geometryangle bisector