Difference between revisions of "2018 JBMO Problems"
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Let <math>\triangle ABC</math> and <math>A'</math>,<math>B'</math>,<math>C'</math> the symmetrics of vertex over opposite sides.The intersection of the circumcircles of <math>\triangle ABB'</math> and <math>\triangle ACC'</math> is <math>A_1</math>.<math>B_1</math> and <math>C_1</math> are defined similarly.Prove that lines <math>AA_1</math>,<math>BB_1</math> and <math>CC_1</math> are concurent. | Let <math>\triangle ABC</math> and <math>A'</math>,<math>B'</math>,<math>C'</math> the symmetrics of vertex over opposite sides.The intersection of the circumcircles of <math>\triangle ABB'</math> and <math>\triangle ACC'</math> is <math>A_1</math>.<math>B_1</math> and <math>C_1</math> are defined similarly.Prove that lines <math>AA_1</math>,<math>BB_1</math> and <math>CC_1</math> are concurent. | ||
Revision as of 06:12, 1 August 2019
Problems/Problem 4
Let 
and 
,
,
the symmetrics of vertex over opposite sides.The intersection of the circumcircles of 
and 
is 
.
and 
are defined similarly.Prove that lines 
,
and 
are concurent.
