MathDB
Weird Geometry

Source: 2019 China TST Test 3 P5

March 29, 2019
geometryincentercircumcircle

Problem Statement

In ΔABC\Delta ABC, AD⊥BCAD \perp BC at DD. E,FE,F lie on line ABAB, such that BD=BE=BFBD=BE=BF. Let I,JI,J be the incenter and AA-excenter. Prove that there exist two points P,QP,Q on the circumcircle of ΔABC\Delta ABC , such that PB=QCPB=QC, and ΔPEI∼ΔQFJ\Delta PEI \sim \Delta QFJ .
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