Problem involving triangle with characterization of midpoints
I have a conjecture which I would like to prove or disprove it.
Question. Given triangle $ABC$. The points $A'$, $B'$, and $C'$ lie on the sides $BC$, $CA$, and $AB$ respectively. Assume that Euler lines of triangles $AB'C'$, $BC'A'$, and $CA'B'$ are parallel. Prove or disprove that $A'$, $B'$, and $C'$ must be midpoints of $BC$, $CA$, and $AB$ respectiely.
geometry euclidean-geometry triangle
asked Nov 24 at 12:46
Tran Quang Hung
1214
add a comment |
I have a conjecture which I would like to prove or disprove it.
Question. Given triangle $ABC$. The points $A'$, $B'$, and $C'$ lie on the sides $BC$, $CA$, and $AB$ respectively. Assume that Euler lines of triangles $AB'C'$, $BC'A'$, and $CA'B'$ are parallel. Prove or disprove that $A'$, $B'$, and $C'$ must be midpoints of $BC$, $CA$, and $AB$ respectiely.
geometry euclidean-geometry triangle
asked Nov 24 at 12:46
Tran Quang Hung
1214
add a comment |
I have a conjecture which I would like to prove or disprove it.
Question. Given triangle $ABC$. The points $A'$, $B'$, and $C'$ lie on the sides $BC$, $CA$, and $AB$ respectively. Assume that Euler lines of triangles $AB'C'$, $BC'A'$, and $CA'B'$ are parallel. Prove or disprove that $A'$, $B'$, and $C'$ must be midpoints of $BC$, $CA$, and $AB$ respectiely.
geometry euclidean-geometry triangle
asked Nov 24 at 12:46
Tran Quang Hung
1214
I have a conjecture which I would like to prove or disprove it.
Question. Given triangle $ABC$. The points $A'$, $B'$, and $C'$ lie on the sides $BC$, $CA$, and $AB$ respectively. Assume that Euler lines of triangles $AB'C'$, $BC'A'$, and $CA'B'$ are parallel. Prove or disprove that $A'$, $B'$, and $C'$ must be midpoints of $BC$, $CA$, and $AB$ respectiely.
geometry euclidean-geometry triangle
geometry euclidean-geometry triangle
asked Nov 24 at 12:46
Tran Quang Hung
1214
asked Nov 24 at 12:46
Tran Quang Hung
1214
asked Nov 24 at 12:46
Tran Quang Hung
1214
asked Nov 24 at 12:46
Tran Quang Hung
1214
asked Nov 24 at 12:46
Tran Quang Hung
1214
1214
add a comment |
add a comment |
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